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
#coding=utf-8
MOD = (10 ** 9) + 7
(A, B, n, x) = map(int, raw_input().split())

res0 = pow(A, n, MOD) * x % MOD
if A == 1:
    res1 = B * n % MOD
else:
    res1 = (pow(A, n, MOD) - 1) * pow(A - 1, MOD - 2, MOD) * B % MOD

#print res0, res1
print (res0 + res1) % MOD

