2149: Iterated Linear Function
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Description
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputConsider 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