# numpyを使った高速化 from typing import List, Dict, Tuple import numpy as np import math def setMebius(n: int) -> np.ndarray: is_prime = np.ones(n + 1, dtype = np.int32) mebius = np.ones(n + 1, dtype = np.int32) is_prime[0] = 0 is_prime[1] = 0 for i in range(2, n + 1): if is_prime[i]: mebius[i : n + 1 : i] *= -1 mebius[i * i : n + 1 : i * i] = 0 is_prime[2 * i : n + 1 : i] = 0 return mebius def calc(L: int, noDiv2: bool, noDiv3: bool, mebius: np.ndarray) -> int: sqL: int = len(mebius) - 1 gs: np.ndarray = np.ones(sqL + 1, dtype = np.int64) * L gs[1::] //= np.arange(1, sqL + 1, dtype = np.int64) * np.arange(1, sqL + 1, dtype = np.int64) if noDiv2 and noDiv3: gs[::2] = 0 gs[::3] = 0 gs = gs - gs // 2 - gs // 3 + gs // 6 elif noDiv2: gs[::2] = 0 gs = gs - gs // 2 elif noDiv3: gs[::3] = 0 gs = gs - gs // 3 return (mebius[1:] * gs[1:]).sum() def subtask4(L: int, a: List[int], mebius: List[int]) -> int: n: int = len(a) plot: List[List[bool]] = [[False for _ in range(60)] for _ in range(60)] for i in range(n): c2: int = 0 c3: int = 0 t: int = a[i] while t % 2 == 0: t //= 2 c2 += 1 while t % 3 == 0: t //= 3 c3 += 1 plot[c2][c3] = True p2: List[int] = [1] p3: List[int] = [1] while p2[-1] <= L: p2.append(p2[-1] * 2) while p3[-1] <= L: p3.append(p3[-1] * 3) ret: int = 0 i: int = 0 mp: Dict[Tuple[int, int, int], int] = {} while p2[i] <= L: j: int = 0 while p2[i] * p3[j] <= L: tmpL: int = L // (p2[i] * p3[j]) # 選ぶ要素のLCM = p2[i] * p3[j] for k in range(16): max2: int = -1 min2: int = 1000000 max3: int = -1 min3: int = 1000000 cnt: int = 0 not_found: bool = False for l in range(4): if (k >> l) % 2 == 1: c2: int = i - l // 2 c3: int = j - l % 2 if c2 < 0 or c3 < 0 or plot[c2][c3] == False: not_found = True break max2 = max(max2, c2) min2 = min(min2, c2) max3 = max(max3, c3) min3 = min(min3, c3) cnt += 1 if not_found or cnt == 0 or max2 != i or max3 != j: continue noDiv2 = (min2 != max2) noDiv3 = (min3 != max3) key = (tmpL, noDiv2, noDiv3) if key not in mp: mp[key] = calc(tmpL, noDiv2, noDiv3, mebius) if cnt % 2 == 1: ret += mp[key] * p2[cnt - 1] else: ret -= mp[key] * p2[cnt - 1] j += 1 i += 1 return ret if __name__ == '__main__': L, N = map(int, input().split()) a = list(map(int, input().split())) sqL: int = 1 while sqL * sqL <= L: sqL += 1 sqL -= 1 mebius: List[int] = setMebius(sqL) ans: int = subtask4(L, a, mebius) print(ans)