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
# from dust i have come, dust i will be

mod=int(1e9)+7

A,B,n,x=map(int,input().split())

'''
if we expand the given formula for some test cases 
e.g-> for n=2,3,4.. we get
A^n*x + B(A^0+A^1+...+A^{n-1})
for the geometric progression, 1+r+r^2+...+r^{n-1}
the ans=(r^n-1)/(r-1) when r>1, if r==1, ans=nr
'''

if n==0:
    print(x)
    exit(0)

if A==1:
    temp=n*A
else:
    '''
    (A/B)%m=(A%m*(B^-1)%m)%m
    '''
    x1=pow(A,n,mod)-1
    x2=pow(A-1,mod-2,mod)
    temp=(x1*x2)% mod

p1=pow(A,n,mod)*pow(x,1,mod)
p1=p1%mod

p2=(B%mod)*temp
p2=p2%mod

print((p1+p2)%mod)
