#!/usr/bin/ python3.8 # %% import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines import numpy as np MOD = 1234567891 N, M, *A = map(int, read().split()) f = np.array([1], np.int64) for x in A: g = np.zeros(len(f) + x, np.int64) g[: len(f)] += f g[x:] -= f f = g % MOD def fft_convolve(f, g, MOD=MOD): """ 数列 (多項式) f, g の畳み込みの計算.上下 15 bitずつ分けて計算することで, 30 bit以下の整数,長さ 250000 程度の数列での計算が正確に行える. """ fft = np.fft.rfft ifft = np.fft.irfft Lf = len(f) Lg = len(g) L = Lf + Lg - 1 fft_len = 1 << L.bit_length() fl = f & (1 << 15) - 1 fh = f >> 15 gl = g & (1 << 15) - 1 gh = g >> 15 def conv(f, g): return ifft(fft(f, fft_len) * fft(g, fft_len))[: L] x = conv(fl, gl) % MOD y = conv(fl + fh, gl + gh) % MOD z = conv(fh, gh) % MOD a, b, c = map(lambda x: (x + .5).astype(np.int64), [x, y, z]) return (a + ((b - a - c) << 15) + (c << 30)) % MOD def coef_of_generating_function(P, Q, N): """compute the coefficient [x^N] P/Q of rational power series. Parameters ---------- P : np.ndarray numerator. Q : np.ndarray denominator Q[0] == 1 and len(Q) == len(P) + 1 is assumed. N : int The coefficient to compute. """ def convolve(f, g): return fft_convolve(f, g, MOD) while N: Q1 = Q.copy() Q1[1:: 2] = np.negative(Q1[1:: 2]) if N & 1: P = convolve(P, Q1)[1:: 2] else: P = convolve(P, Q1)[:: 2] Q = convolve(Q, Q1)[:: 2] N >>= 1 return P[0] P = np.zeros(len(f) - 1, np.int64) P[0] = 1 answer = coef_of_generating_function(P, f, M) print(answer)