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
a, b, n, x = map(int, raw_input().split())
p = 10**9+7
'''
for k in range(n):
    now = (a*pre+b) % p
    pre = now
print now % p
'''
def sum_(x,n):
    if n == 0:
        return 1
    elif n & 1:
        return (1 + pow(x, (n + 1) / 2, p)) * sum_(x, (n - 1) / 2) % p
    else:
        return ((1 +pow(x, n / 2, p)) * sum_(x, n / 2 - 1) % p + pow(x, n, p)) % p


res = x * pow(a, n, p) % p + b * sum_(a, n-1) % p
print res % p
 	 	  	 				  		 			 	   		 	 	