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  
def modInverse(b,m): 
    g = math.gcd(b, m)  
    if (g != 1):   
        return -1
    else:    
        return pow(b, m - 2, m) 
def modDivide(a,b,m): 
    a = a % m 
    inv = modInverse(b,m) 
    return (inv*a)%m 
mod=int(10e8+7)
a,b,n,x=map(int,input().split())
if a==1:
    print((x%mod+(n*b)%mod)%mod)
    exit()
exp=a
ans=1
while n>0:
    if(n%2==1):
        ans=(ans*exp)%mod
    exp=(exp*exp)%mod
    n//=2  
res=(ans-1)%mod
res=modDivide(res,a-1,mod)
print(((ans*x)%mod+(res*b)%mod)%mod)
