codeforces_678D. Iterated Linear Function（快速幂）

D. Iterated Linear Function

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 longinteger 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

快速幂求等比数列之和就行，不过取模要注意一下，除法需要用到逆元。

a^(mod) % mod = a

a^(mod-1) % mod = 1

a^(mod-2) * a %mod = 1

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include