結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー toyuzuko
提出日時 2020-07-25 19:35:23
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 84 ms / 5,000 ms
コード長 2,033 bytes
コンパイル時間 1,109 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 76,416 KB
最終ジャッジ日時 2024-06-27 13:44:08
合計ジャッジ時間 4,303 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 37
権限があれば一括ダウンロードができます

ソースコード

diff # 

from itertools import accumulate

MOD = 1000000007

N, K = map(int, input().split())
A = list(map(int, input().split()))
C = [0] + list(accumulate(A))

if N <= 10000 and K <= 1000000:
    res = [0 for _ in range(K)]
    for i in range(N):
        res[i] = A[i]
    res[N] = sum(A)
    for i in range(N + 1, K):
        res[i] = res[i - 1] * 2 - res[i - N - 1]
        res[i] %= MOD
    print(res[-1], sum(res) % MOD)

else:
    def inc(arr, base):
        n = len(arr)
        res = [0 for _ in range(n)]
        res[0] = arr[n - 1] * base[0]
        for i in range(1, n):
            res[i] = arr[i - 1] + arr[n - 1] * base[i]
            res[i] %= MOD
        return res

    def dec(arr, base):
        n = len(arr)
        res = [0 for _ in range(n)]
        res[n - 1] = arr[0] * pow(base[0], MOD - 2, MOD)
        for i in range(n - 1)[::-1]:
            res[i] = arr[i + 1] - res[n - 1] * base[i + 1]
            res[i] %= MOD
        return res

    def dub(arr, base):
        n = len(arr)
        res = [0 for _ in range(n)]
        tmp = [arr]
        for i in range(n - 1):
            tmp.append(inc(tmp[-1], base))
        for i in range(n):
            for j in range(n):
                res[i] += tmp[0][j] * tmp[j][i]
                res[i] %= MOD
        return res

    res = [1 for _ in range(N)]
    exp = K - 1

    base = [1 for _ in range(N)]

    for _ in range(N):
        res = dec(res, base)

    for bit in range(exp.bit_length())[::-1]:
        res = dub(res, base)
        if (exp >> bit) & 1:
            res = inc(res, base)

    F = sum([res[i] * A[i] for i in range(N)]) % MOD

    res = [0 for _ in range(N + 1)]
    res[0] = -1
    res[-1] = 2
    base = [0 for _ in range(N + 1)]
    base[0] = -1
    base[-1] = 2
    exp = K

    for _ in range(N + 1):
        res = dec(res, base)

    for bit in range(exp.bit_length())[::-1]:
        res = dub(res, base)
        if (exp >> bit) & 1:
            res = inc(res, base)

    S = sum([res[i] * C[i] for i in range(N + 1)]) % MOD

    print(F, S)
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