class Matrix(object): def __init__(self, nrow=1, ncol=1): self.nrow = nrow self.ncol = ncol self._data = [[0] * nrow for c in range(ncol)] def from2Dlist(self, data): self.nrow = len(data) self.ncol = len(data[0]) for row in data: if len(row) != self.ncol: raise IndexError('All column lengths must be same.') self._data = [[val for val in row] for row in data] return self def __getitem__(self, key): row, col = key return self._data[row][col] def __setitem__(self, key, value): row, col = key self._data[row][col] = value def __add__(self, other): if self.nrow != other.nrow or self.ncol != other.ncol: raise TypeError('lhs and rhs must be same size.') mat = [] for row1, row2 in zip(self._data, other._data): row = [a + b for a, b in zip(row1, row2)] mat.append(row) return Matrix().from2Dlist(mat) def __sub__(self, other): if self.nrow != other.nrow or self.ncol != other.ncol: raise TypeError('lhs and rhs must be same size.') mat = [] for row1, row2 in zip(self._data, other._data): row = [a - b for a, b in zip(row1, row2)] mat.append(row) return Matrix().from2Dlist(mat) def __mul__(self, other): '''行列の積を求める。要素毎の乗算ではない。 ''' mod = 10 ** 9 + 7 if self.ncol != other.nrow: raise TypeError('ncol of lhs and nrow of rhs must be same.') mat = [] mat2 = other._data n = other.ncol for row1 in self._data: row = [sum(a * b[i] for a, b in zip(row1, mat2)) % mod for i in range(n)] mat.append(row) return Matrix().from2Dlist(mat) def __imul__(self, other): self = self.__mul__(other) return self def __str__(self): return '\n'.join(map(str, self._data)) def read_data(): N, K = map(int, input().split()) As = list(map(int, input().split())) return N, K, As def solve(N, K, As): if K <= 10**6: return solve2(N, K, As) else: return solve3(N, K, As) def solve2(N, K, As): mod = 10**9 + 7 As.append(sum(As) % mod) idx = N cum = sum(As) % mod for i in range(1, K - N): new_idx = (idx + 1) % (N + 1) As[new_idx] = (2 * As[idx] - As[new_idx]) % mod cum += As[new_idx] cum %= mod idx = new_idx return As[idx], cum def solve3(N, K, As): mod = 10 ** 9 + 7 if K <= N: return As[K - 1] data = [[1] * N] for n in range(N-1): row = [0] * N row[n] = 1 data.append(row) dataI = [[0] * N for i in range(N)] for n in range(N): dataI[n][n] = 1 mat = Matrix().from2Dlist(data) mat2 = Matrix().from2Dlist(dataI) K = K - N while K: if K & 1: mat2 *= mat mat *= mat K >>= 1 fk = sum(mat2[0, i] * ai for i, ai in enumerate(As[::-1])) % mod mat = Matrix().from2Dlist(data) matI = Matrix().from2Dlist(dataI) mat3 = mat2 * mat - matI inv = inverse(N) inv *= mat3 sk = (sum(inv[0, i] * ai for i, ai in enumerate(As[::-1]))//(N - 1) + sum(As[:-1])) % mod return fk, sk def inverse(n): ''' 1/5(1,5, 4, 3, 2, 1) (1,0, 4, 3, 2, 1) (1,0,-1, 3, 2, 1) (1,0,-1,-2, 2, 1) (1,0,-1,-2,-3, 1) (1,0,-1,-2,-3,-4) ''' row = [i for i in range(N, 0, -1)] data = [row[:] for i in range(n)] m = n - 1 for i in range(n): for j in range(i + 1): data[i][j] -= m return Matrix().from2Dlist(data) N, K, As = read_data() print(*solve(N, K, As))