import numpy as np import sys from collections import defaultdict, Counter, deque from itertools import permutations, combinations, product, combinations_with_replacement, groupby, accumulate import operator from math import sqrt, gcd, factorial # from math import isqrt, prod,comb # python3.8用(notpypy) #from bisect import bisect_left,bisect_right #from functools import lru_cache,reduce #from heapq import heappush,heappop,heapify,heappushpop,heapreplace #import numpy as np #import networkx as nx #from networkx.utils import UnionFind #from numba import njit, b1, i1, i4, i8, f8 #from scipy.sparse import csr_matrix #from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson, NegativeCycleError # numba例 @njit(i1(i4[:], i8[:, :]),cache=True) 引数i4配列、i8 2次元配列,戻り値i1 def input(): return sys.stdin.readline().rstrip() def divceil(n, k): return 1+(n-1)//k # n/kの切り上げを返す def yn(hantei, yes='Yes', no='No'): print(yes if hantei else no) def dot(a, b, n, mod=10**9+7): """ 正方行列積a@bの10**9+7modをオーバーフロー回避するために分割して掛け算する """ ans = np.zeros_like(a, dtype=np.int64) newn = ((n//8+1)*8) a2 = np.zeros((newn, newn), dtype=np.int64) a2[0:n, 0:n] += a b2 = np.zeros((newn, newn), dtype=np.int64) b2[0:n, 0:n] += b ans = np.zeros_like(a2, dtype=np.int64) for k in range(newn//8): for i in range(newn//8): for j in range(newn//8): ans[i*8:i*8+8, j*8:j*8+8] += a2[i*8:i*8+8, k*8:k*8+8] @ b2[k*8:k*8+8, j*8:j*8+8] ans[i*8:i*8+8, j*8:j*8+8] %= mod return ans[0:n, 0:n] def dot2(mat1, mat2, MOD): """ 行列積a@bの10**9+7modをオーバーフロー回避するために上下15bitで分割して掛け算する https://ikatakos.com/pot/programming_algorithm/python_tips/avoid_overflow """ mask = (1 << 15) - 1 mat1h = mat1 >> 15 mat1l = mat1 & mask mat2h = mat2 >> 15 mat2l = mat2 & mask mathh = mat1h @ mat2h % MOD matll = mat1l @ mat2l % MOD mathl = (mathh + matll - (mat1h - mat1l) @ (mat2h - mat2l)) % MOD res = (mathh << 30) + (mathl << 15) + matll res %= MOD return res def matrix_multiplication(a, n, k, mod=10**9+7): # n次正方行列a^k ans = np.eye(n, dtype=np.int64) while k: k, i = divmod(k, 2) if i: ans = dot2(ans, a, mod) a = dot2(a, a, mod) return ans def main(): mod = 10**9+7 mod2 = 998244353 p, q, r, k = map(int, input().split()) mat = np.zeros((3, 3), dtype=np.int64) mat[1][0] = 1 mat[2][1] = 1 mat[0][2] = 1 mat[1][2] = 1 mat[2][2] = 1 mat=matrix_multiplication(mat,3,k-1,10) print(dot2(np.array([p,q,r],dtype=np.int64),mat,10)[0]) if __name__ == '__main__': main()