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,input().split())
mod=(10**9+7)*(a-1)
mod1=(10**9+7)
#print(int(x*(a**n)+b*(a**n-1)/(a-1)))'''
def bin_pow(a,n,mod):
    if n==1:
        return a
    else:
        if n%2==0:
            return ((bin_pow(a,n//2,mod)**2))%mod
        return (((bin_pow(a,n//2,mod)**2)*a))%mod

        
def s(a,n,b=1):
    ans=0
    for k in range(n):
        ans+=b*(a**k)
    return ans
 
if a!=1:
    ans=x*bin_pow(a,n,mod)

    ans+=b*(bin_pow(a,n,mod)-1)//(a-1)   
    print(int(ans)%mod1)

else:
    ans=x*bin_pow(a,n,mod1)
    ans+=b*n
    print(ans%mod1)
