import sys readline = sys.stdin.readline ns = lambda: readline().rstrip() ni = lambda: int(readline().rstrip()) nm = lambda: map(int, readline().split()) nl = lambda: list(map(int, readline().split())) def Kitamasa(C, X, k, e0=0, e1=1, mod=10**9+7): ''' 0-indexed calc X[k] ''' n = len(X) def _plus1(g): ret = [(g[i-1] + g[-1] * C[i]) % mod for i in range(n)] ret[0] = g[-1] * C[0] % mod return ret def _mult2(g): ret = [e0]*(2 * n - 1) for i in range(n): for j in range(n): ret[i + j] = (ret[i + j] + g[i] * g[j]) % mod for i in range(2*n-2, n-1, -1): for j in range(n): ret[i + j - n] = (ret[i + j - n] + ret[i] * C[j]) % mod return ret[:n] g = [e0]*n g[0] = e1 t = k.bit_length() for i in range(t-1, -1, -1): g = _mult2(g) if k & (1<