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 sys
input = sys.stdin.readline

a,b,n,x = (int(i) for i in input().split())
m = int(1e9) + 7
ans = (pow(a,n,m) * x) % m
if a > 1:
    # ans += ((((1/(1-a) - (pow(a,n,10**100)/(1-a))) ) % m) * b) % m
    # ans += ((( (1/(1-a)) + (pow(a,n,a**n + 1)/(1-a)) ) % m) * b) % m
    # ans += ((pow(a,n,m)-1)/(a+1)*b) % m
    ans += ((((pow(a,n,m*(a-1))-1)/(a-1))) * b) % m
elif a==0:
    ans += b
elif a==1:
    ans += n*b % m
print(ans % m)