[Gold IV] Title: 지수를 더하자, Time: 96 ms, Memory: 95364 KB -BaekjoonHub

Author: 051198Hz

백준/Gold/27725. 지수를 더하자/README.md

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+# [Gold IV] 지수를 더하자 - 27725 
+
+[문제 링크](https://www.acmicpc.net/problem/27725) 
+
+### 성능 요약
+
+메모리: 95364 KB, 시간: 96 ms
+
+### 분류
+
+수학, 정수론
+
+### 제출 일자
+
+2026년 1월 25일 16:36:48
+
+### 문제 설명
+
+<p>서로 다른 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>개의 소수로 이루어진 집합 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c7B"></mjx-c></mjx-mo><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msub><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-msub space="2"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msub><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c22EF"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-msub space="2"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msub><mjx-mo class="mjx-n"><mjx-c class="mjx-c7D"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo fence="false" stretchy="false">}</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$P=\{p_{1}, p_{2}, \cdots, p_{N}\}$</span></mjx-container>이 있다.</p>
+
+<p>양의 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i$</span></mjx-container>에 대하여 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-mrow size="s"><mjx-msubsup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.297em; margin-left: 0px;"><mjx-texatom size="s" texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.312em;"><mjx-texatom texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msub></mjx-texatom><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msubsup><mjx-mo class="mjx-n"><mjx-c class="mjx-cD7"></mjx-c></mjx-mo><mjx-msubsup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.297em; margin-left: 0px;"><mjx-texatom size="s" texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.312em;"><mjx-texatom texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msub></mjx-texatom><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msubsup><mjx-mo class="mjx-n"><mjx-c class="mjx-cD7"></mjx-c></mjx-mo><mjx-mo class="mjx-n"><mjx-c class="mjx-c22EF"></mjx-c></mjx-mo><mjx-mo class="mjx-n"><mjx-c class="mjx-cD7"></mjx-c></mjx-mo><mjx-msubsup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.309em; margin-left: 0px;"><mjx-texatom size="s" texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.329em;"><mjx-texatom texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msub></mjx-texatom><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msubsup></mjx-mrow></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>i</mi><mrow><msubsup><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></msubsup><mo>×</mo><msubsup><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msubsup><mo>×</mo><mo>⋯</mo><mo>×</mo><msubsup><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow><mrow data-mjx-texclass="ORD"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mrow></msubsup></mrow></mfrac></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$\frac{i}{p_{1}^{a_{1}}\times p_{2}^{a_{2}}\times \cdots \times p_{N}^{a_{N}}}$</span></mjx-container>의 값이 양의 정수가 되도록 하는 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-munderover limits="false"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c2211 TEX-S1"></mjx-c></mjx-mo><mjx-script style="vertical-align: -0.285em; margin-left: 0px;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-spacer style="margin-top: 0.291em;"></mjx-spacer><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D457 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-munderover><mjx-texatom space="2" texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D457 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$\sum_{j=1}^{N}{a_{j}}$</span></mjx-container>의 최댓값을 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mi>i</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$b_i$</span></mjx-container>라고 하자. (단, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D457 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$a_{j}$</span></mjx-container>는 정수이다.)</p>
+
+<p>집합 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$P$</span></mjx-container>와 양의 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$K$</span></mjx-container>가 주어질 때, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-munderover limits="false"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c2211 TEX-S1"></mjx-c></mjx-mo><mjx-script style="vertical-align: -0.285em; margin-left: 0px;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-spacer style="margin-top: 0.291em;"></mjx-spacer><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-munderover><mjx-msub space="2"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></munderover><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$\sum_{i=1}^{K} b_{i}$</span></mjx-container>의 값을 구하시오.</p>
+
+### 입력 
+
+ <p>첫째 줄에 집합 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$P$</span></mjx-container>의 원소의 개수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi><mjx-mrow space="2"><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c32"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-mrow></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>200</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>000</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N\left(1\leq N \leq 200\,000\right)$</span></mjx-container>가 주어진다.</p>
+
+<p>둘째 줄에 집합 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$P$</span></mjx-container>를 이루는 서로 다른 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>개의 소수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-mrow space="2"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c28 TEX-S1"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D45D TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c33"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-cD7"></mjx-c></mjx-mo><mjx-msup space="3"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-script style="vertical-align: 0.393em;"><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c36"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msup><mjx-mo class="mjx-sop"><mjx-c class="mjx-c29 TEX-S1"></mjx-c></mjx-mo></mjx-mrow></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow data-mjx-texclass="ORD"><mn>6</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$p\left(1\leq p \leq 3\times 10^{6}\right)$</span></mjx-container>가 공백을 두고 주어진다.</p>
+
+<p>셋째 줄에 양의 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi><mjx-mrow space="2"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c28 TEX-S1"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-msup space="4"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-script style="vertical-align: 0.393em;"><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-msup><mjx-mo class="mjx-sop"><mjx-c class="mjx-c29 TEX-S1"></mjx-c></mjx-mo></mjx-mrow></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>≤</mo><mi>K</mi><mo>≤</mo><msup><mn>10</mn><mrow data-mjx-texclass="ORD"><mn>12</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$K\left(1\leq K \leq 10^{12}\right)$</span></mjx-container>가 주어진다.</p>
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+### 출력 
+
+ <p><mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"> <mjx-math class="MJX-TEX" aria-hidden="true"><mjx-munderover limits="false"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c2211 TEX-S1"></mjx-c></mjx-mo><mjx-script style="vertical-align: -0.285em; margin-left: 0px;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-spacer style="margin-top: 0.291em;"></mjx-spacer><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom></mjx-script></mjx-munderover><mjx-msub space="2"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></munderover><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$\sum_{i=1}^{K} b_{i}$</span></mjx-container>의 값을 출력하시오.</p>
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