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
import math
import sys
sys.setrecursionlimit(10000)
def gcd(a, b):
    return b if a % b == 0 else gcd(b, a % b)

def lcm(a, b):
    return a*b/gcd(a,b)

def e_gcd(a, b):
    if (a == 0):
        return 0, 1, b
    x1, y1, d = e_gcd(b % a, a)
    x = y1 - (b / a) * x1
    y = x1
    return x, y, d

s = raw_input()
a, b, n, x = s.split()
a = int(a)
b = int(b)
n = int(n)
x = int(x)

base = int(1e9 + 7)
if a == 1:
    print (x + (n)*b)%base
else:
    
    res = (pow(a, n, base) * x) % base
    
    s = (b * (1 - pow(a, n, base))) % base
    s = (s + base) % base
    
    q = (1 - a) % base + base
    q %= base
    xx, yy, dd = e_gcd(q, base)
    xx = (xx % base + base) % base
    ans = res + s * xx
    print ans % base



