Problem1920--Iterated Linear Function

1920: Iterated Linear Function

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79

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