結果

問題 No.194 フィボナッチ数列の理解(1)
コンテスト
ユーザー lam6er
提出日時 2025-03-20 20:44:58
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 89 ms / 5,000 ms
コード長 2,798 bytes
コンパイル時間 217 ms
コンパイル使用メモリ 82,384 KB
実行使用メモリ 81,684 KB
最終ジャッジ日時 2025-03-20 20:45:06
合計ジャッジ時間 3,880 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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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 # 

import sys
from collections import deque

MOD = 10**9 + 7

def build_transition_matrix(n):
    size = n + 1
    T = [[0] * size for _ in range(size)]
    # Row 0: sum of first N elements
    for j in range(n):
        T[0][j] = 1
    # Rows 1 to n-1: shifted
    for i in range(1, n):
        T[i][i-1] = 1
    # Row n: sum of first N and 1 in column n
    for j in range(n):
        T[n][j] = 1
    T[n][n] = 1
    return T

def matrix_mult(a, b, mod):
    n = len(a)
    m = len(b[0])
    p = len(b)
    result = [[0] * m for _ in range(n)]
    for i in range(n):
        for k in range(p):
            if a[i][k] == 0:
                continue
            for j in range(m):
                result[i][j] = (result[i][j] + a[i][k] * b[k][j]) % mod
    return result

def matrix_pow(mat, power, mod):
    n = len(mat)
    result = [[0] * n for _ in range(n)]
    for i in range(n):
        result[i][i] = 1  # Identity matrix
    while power > 0:
        if power % 2 == 1:
            result = matrix_mult(result, mat, mod)
        mat = matrix_mult(mat, mat, mod)
        power //= 2
    return result

def matrix_vector_mult(mat, vec, mod):
    size = len(vec)
    result = [0] * size
    for i in range(size):
        for j in range(size):
            result[i] = (result[i] + mat[i][j] * vec[j]) % mod
    return result

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    K = int(input[ptr])
    ptr += 1
    A = list(map(int, input[ptr:ptr+N]))
    ptr += N

    if K <= N:
        F = A[K-1] % MOD
        S = sum(A[:K]) % MOD
    else:
        sum_initial = sum(A) % MOD
        if N <= 30:
            # Matrix exponentiation approach
            reversed_A = list(reversed(A))
            initial = [a % MOD for a in reversed_A]
            initial.append(sum_initial % MOD)
            T = build_transition_matrix(N)
            power = K - N
            T_power = matrix_pow(T, power, MOD)
            result_state = matrix_vector_mult(T_power, initial, MOD)
            F = result_state[0] % MOD
            S = result_state[-1] % MOD
        else:
            # Deque approach
            deque_list = deque()
            for a in A:
                deque_list.append(a % MOD)
            deque_list.append(sum_initial % MOD)
            steps_needed = K - (N + 1)
            S = (sum_initial * 2) % MOD
            for _ in range(steps_needed):
                current_last = deque_list[-1]
                first = deque_list.popleft()
                new_F = (2 * current_last - first) % MOD
                new_F = (new_F + MOD) % MOD  # Ensure non-negative
                S = (S + new_F) % MOD
                deque_list.append(new_F)
            F = deque_list[-1] % MOD
    print(F, S)

if __name__ == "__main__":
    main()
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