Submission #13759276

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Source Code Expand

import sys
import numpy as np

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

MOD = 10**9 + 7

N, M = map(int, read().split())

def make_power(a, L, MOD=MOD):
    B = L.bit_length()
    x = np.empty(1 << B, np.int64)
    x[0] = 1
    for n in range(B):
        x[1 << n:1 << (n + 1)] = x[:1 << n] * a % MOD
        a *= a
        a %= MOD
    x = x[:L]
    x.flags.writeable = False
    return x

pow2 = make_power(2, M + 10)
ipow2 = make_power((1 + MOD) // 2, M + 10)

def update(dp):
    B = dp.copy()
    C = dp * np.arange(M + 1) % MOD * ipow2[:M + 1] % MOD
    dp[1:] = np.cumsum(C[:-1]) % MOD
    dp[1:] *= pow2[:M]
    dp %= MOD
    dp += np.arange(1, M + 2) * B
    dp %= MOD

dp = pow2[:M + 1].copy()
for _ in range(N - 1):
    update(dp)

print(dp[-1])

Submission Info

Judge Result