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:utf8

def qp(a, b, m):
    res = 1
    while b > 0:
        if b % 2 == 1:
            res = (res * a) % m
        b >>= 1
        a = (a * a) % m

    return res


_str = input()
a, b, n, x = [int(x) for x in _str.split(" ")]
m = 10**9 + 7

res = 0
am = qp(a, n, m)


def ext_ru(a, b, m):
    r = qp(b, m - 2, m)
    return (a * r) % m

c1 = am - 1
c2 = a - 1

if c2 == 0:
    print((x % m + ((b % m) * (n % m)) % m) % m)
    exit(0)
else:
    _dev = ext_ru(c1, c2, m)
    res = (((am % m) * (x % m)) % m + ((b % m) * (_dev % m)) % m) % m
    print(int(res))
    exit(0)
 			  	    		 	 					 		 			  	