|
| 1 | +import math |
| 2 | +import sys |
| 3 | + |
| 4 | +read = lambda: sys.stdin.readline().rstrip() |
| 5 | + |
| 6 | + |
| 7 | +class Problem: |
| 8 | + def __init__(self): |
| 9 | + self.n, self.w = map(int, read().split()) |
| 10 | + self.inner, self.outer = list(map(int, read().split())), list(map(int, read().split())) |
| 11 | + |
| 12 | + def solve(self) -> None: |
| 13 | + if self.n == 1: |
| 14 | + print(2 - int(self.inner[0] + self.outer[0] <= self.w)) |
| 15 | + return |
| 16 | + |
| 17 | + minimum = min( |
| 18 | + self.find_minimum( |
| 19 | + [[1, 1, 2 - int(self.inner[0] + self.outer[0] <= self.w)]] + [[0, 0, 0] for _ in range(self.n - 1)], |
| 20 | + self.inner[:], |
| 21 | + self.outer[:], |
| 22 | + )[-1][2], |
| 23 | + ( |
| 24 | + math.inf |
| 25 | + if self.inner[-1] + self.inner[0] > self.w |
| 26 | + else self.find_minimum( |
| 27 | + [[1, 1, 2]] + [[0, 0, 0] for _ in range(self.n - 1)], |
| 28 | + [math.inf] + self.inner[1:-1] + [math.inf], |
| 29 | + self.outer[:], |
| 30 | + )[-1][1] |
| 31 | + ), |
| 32 | + ( |
| 33 | + math.inf |
| 34 | + if self.outer[-1] + self.outer[0] > self.w |
| 35 | + else self.find_minimum( |
| 36 | + [[1, 1, 2]] + [[0, 0, 0] for _ in range(self.n - 1)], |
| 37 | + self.inner[:], |
| 38 | + [math.inf] + self.outer[1:-1] + [math.inf], |
| 39 | + )[-1][0] |
| 40 | + ), |
| 41 | + ( |
| 42 | + math.inf |
| 43 | + if (self.inner[-1] + self.inner[0] > self.w) or (self.outer[-1] + self.outer[0] > self.w) |
| 44 | + else self.find_minimum( |
| 45 | + [[1, 1, 2]] + [[0, 0, 0] for _ in range(self.n - 1)], |
| 46 | + [math.inf] + self.inner[1:-1] + [math.inf], |
| 47 | + [math.inf] + self.outer[1:-1] + [math.inf], |
| 48 | + )[-2][2] |
| 49 | + ), |
| 50 | + ) |
| 51 | + |
| 52 | + print(minimum) |
| 53 | + |
| 54 | + def find_minimum(self, dp: list[list[int]], inner: list[float], outer: list[float]) -> list[list[int]]: |
| 55 | + for idx in range(1, self.n): |
| 56 | + inner_count = 2 - int(inner[idx - 1] + inner[idx] <= self.w) |
| 57 | + outer_count = 2 - int(outer[idx - 1] + outer[idx] <= self.w) |
| 58 | + vertical_count = 2 - int(inner[idx] + outer[idx] <= self.w) |
| 59 | + |
| 60 | + dp[idx] = [ |
| 61 | + min(dp[idx - 1][1] + inner_count, dp[idx - 1][2] + 1), |
| 62 | + min(dp[idx - 1][0] + outer_count, dp[idx - 1][2] + 1), |
| 63 | + min( |
| 64 | + dp[idx - 2][2] + inner_count + outer_count, |
| 65 | + dp[idx - 1][0] + outer_count + 1, |
| 66 | + dp[idx - 1][1] + inner_count + 1, |
| 67 | + dp[idx - 1][2] + vertical_count, |
| 68 | + ), |
| 69 | + ] |
| 70 | + |
| 71 | + return dp |
| 72 | + |
| 73 | + |
| 74 | +if __name__ == "__main__": |
| 75 | + for _ in range(int(read())): |
| 76 | + Problem().solve() |
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