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
global mod
mod=10**9+7
def power(x, y, p) :
    res = 1     # Initialize result

    # Update x if it is more
    # than or equal to p
    x = x % p

    while (y > 0) :

        # If y is odd, multiply
        # x with result
        if ((y & 1) == 1) :
            res = (res * x) % p

        # y must be even now
        y = y >> 1      # y = y/2
        x = (x * x) % p

    return res
def sol(a,b,x,n):
    if a==1:
        return (x+b*n)%mod
    an=power(a,n,mod)

    r=power((1-a),mod-2,mod)
    r=(r%mod*(1-an)%mod)%mod
    r=r*b%mod
    r=r%mod

    f=r+(an%mod*x%mod)%mod
    f=f%mod

    return int(f)
a,b,n,x=list(map(int,input().split()))
print(sol(a,b,x,n))
""""
10000 10000 1000000000000000 10000
"""
