import copy class matrix(): def __init__(self): self.mod = 10**9+7 def multiplication(self,arr1,arr2): ''' 例 arr1 2 3 4 5 6 7 8 9 arr2 1 2 3 4 5 6 7 8 ''' H = len(arr1) W = len(arr2[0]) arr3 = [[0]*W for i in range(H)] for i in range(H): for j in range(W): val = 0 for k in range(len(arr1[0])): val += arr1[i][k]*arr2[k][j] arr3[i][j] = val return arr3 def determinant(self,arr): ''' 正方行列N*Nの行列式 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) N = len(arr_calc) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]/d for k in range(i,N): arr_calc[j][k] -= e*arr_calc[i][k] #arr_calc 上△行列 det = 1 for i in range(N): det *= arr_calc[i][i] return det def invarr(self,arr): ''' 正方行列N*Nの逆行列 det == 0ならreturn False 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) if self.determinant(arr_calc) == 0: return False N = len(arr_calc) for i in range(N): v = [0]*(N) v[i] = 1 arr_calc[i].extend(v) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]/d for k in range(i,2*N): arr_calc[j][k] -= e*arr_calc[i][k] for i in range(N-1,-1,-1): d = arr_calc[i][i] for k in range(i,2*N): arr_calc[i][k] /= d for j in range(i-1,-1,-1): c = arr_calc[j][i] for k in range(i,2*N): arr_calc[j][k] -= c*arr_calc[i][k] inv = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): inv[i][j] = arr_calc[i][j+N] return inv def SimultaneousE(self,arr): ''' 3x+2y+z = 4 4x+5y+6z = 3 7x+8y+9z = 2 -> 3 2 1 4 4 5 6 3 7 8 9 2 ''' N = len(arr) arr1 = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): arr1[i][j] = arr[i][j] v = [[0] for i in range(N)] for i in range(N): v[i][0] = arr[i][-1] if self.determinant(arr1) == 0: return False inva = self.invarr(arr1) return self.multiplication(inva,v) def invmod(self,a):#mod逆元 if a == 0: return 0 if a == 1: return 1 return (-self.invmod(self.mod % a) * (self.mod // a)) % self.mod def multiplication_mod(self,arr1,arr2): H = len(arr1) W = len(arr2[0]) arr3 = [[0]*W for i in range(H)] for i in range(H): for j in range(W): val = 0 for k in range(len(arr1[0])): val += arr1[i][k]*arr2[k][j] arr3[i][j] = val%self.mod return arr3 def determinant_mod(self,arr): ''' 正方行列N*Nの行列式 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) N = len(arr_calc) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]*self.invmod(d) e %= self.mod for k in range(i,N): arr_calc[j][k] -= e*arr_calc[i][k] arr_calc[j][k] %= self.mod #arr_calc 上△行列 det = 1 for i in range(N): det *= arr_calc[i][i] det %= self.mod return det def invarr_mod(self,arr): ''' 正方行列N*Nの逆行列 det == 0ならreturn False 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) det = self.determinant_mod(arr_calc) if det == 0: return False N = len(arr_calc) for i in range(N): v = [0]*(N) v[i] = det arr_calc[i].extend(v) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]*self.invmod(d) for k in range(i,2*N): arr_calc[j][k] -= e*arr_calc[i][k] arr_calc[j][k] %= self.mod for i in range(N-1,-1,-1): d = arr_calc[i][i] for k in range(i,2*N): arr_calc[i][k] *= self.invmod(d) for j in range(i-1,-1,-1): c = arr_calc[j][i] for k in range(i,2*N): arr_calc[j][k] -= c*arr_calc[i][k] arr_calc[j][k] %= self.mod inv = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): inv[i][j] = arr_calc[i][j+N]*self.invmod(det)%self.mod return inv def SimultaneousE_mod(self,arr): ''' 3x+2y+z = 4 4x+5y+6z = 3 7x+8y+9z = 2 -> 3 2 1 4 4 5 6 3 7 8 9 2 ''' N = len(arr) arr1 = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): arr1[i][j] = arr[i][j] v = [[0] for i in range(N)] for i in range(N): v[i][0] = arr[i][-1] det = self.determinant_mod(arr1) if det == 0: return False inva = self.invarr_mod(arr1) v2 = self.multiplication_mod(inva,v) for i in range(N): v2[i][0] %= self.mod return v2 def modPow_matrix(self,arr,n): ''' N*Nの正方行列arrをn乗する。 ''' N = len(arr) if n==0: arr1 = [[0]*(N) for i in range(N)] for i in range(N): arr1[i][i] = 1 return arr1 if n==1: for i in range(N): for j in range(N): arr[i][j] %= self.mod return arr if n % 2 == 1: arr2 = self.multiplication_mod(arr,self.modPow_matrix(arr,n-1)) return arr2 arr3 = self.modPow_matrix(arr,n//2) return self.multiplication_mod(arr3,arr3) def Pow_matrix(self,arr,n): ''' N*Nの正方行列arrをn乗する。 ''' N = len(arr) if n==0: arr1 = [[0]*(N) for i in range(N)] for i in range(N): arr1[i][i] = 1 return arr1 if n==1: return arr if n % 2 == 1: arr2 = self.multiplication(arr,self.Pow_matrix(arr,n-1)) return arr2 arr3 = self.Pow_matrix(arr,n//2) return self.multiplication(arr3,arr3) a,b,n = map(int,input().split()) arr = [[a,b],[1,0]] MT = matrix() arr2 = MT.modPow_matrix(arr, n) vec = [[1],[0]] vec2 = MT.multiplication_mod(arr2, vec) print(vec2[1][0])