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
#迭代
def quick_pow(a,n,mod):
    ans = 1
    while(n):
        if(n & 1):    ans = ans * a % mod
        a = a * a % mod
        n =n >> 1
    return ans

A, B, n, x = list(map(int,input().split()))
mod = 1000000000+7
if (A == 1):    ans = (x + n*B) % mod
else:
    A_n = quick_pow(A,n,mod)
    ans = (A_n * x + B * (1 - A_n)%mod*quick_pow(1-A,mod-2,mod)) % mod
print(ans)

	  	 	 				 			     				   	 		