Day 165-Q1 — 2026-09-29 | 引き算ゲームの Grundy 数列の周期（引ける個数の集合 S・N が $10^{18}$）

📋 コピーimport sys
def grundy_cycle(S):
    m = max(S); g = []; seen = {}
    # g[i] for i>=0; window = last m values (padded: values for negative idx never used since moves need a<=n)
    n = 0
    while True:
        used = {g[n-a] for a in S if a <= n}
        v = 0
        while v in used: v += 1
        g.append(v); n += 1
        if n >= m:
            key = tuple(g[n-m:n])
            if key in seen:
                s = seen[key]      # window ending at index s-1 equals window ending at n-1
                return g, s - m, n - s   # pre = first index of periodic part? see below
            seen[key] = n
def gval(g, pre_end, period, x):
    # g[i] == g[i+period] for i >= pre_end
    if x < len(g): return g[x]
    return g[pre_end + (x - pre_end) % period]
def main():
    data = sys.stdin.read().split(); k, t = int(data[0]), int(data[1])
    S = sorted(map(int, data[2:2+k])); xs = data[2+k:2+k+t]
    g, pre, per = grundy_cycle(S)
    out = []
    for x in xs:
        out.append(gval(g, pre, per, int(x)))
    # XOR
    r = 0
    for v in out: r ^= v
    print("First" if r else "Second")
main()