考虑一个线性函数 f(x) = Ax + B。让我们定义 g(0)(x) = x 和 g(n)(x) = f(g(n - 1)(x)) 对于 n > 0。对于给定的整数值 A, B, nand x 找到 g(n)(x) 模 109 + 7 的值。
Consider a linear function f(x)=Ax+B. Let's define g(0)(x)=x and g(n)(x)=f(g(n-1)(x)) for n>0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109+7.
Input
The only line contains four integers A, B, n and x (1≤A,B,x≤109,1≤n≤1018) − the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s − the value g(n)(x) modulo 109+7.