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

m = long(1000000007)
#pow(w^y)

def getpowmod(w,y):
    powai = []
    i = long(1)
    t = w
    while i <= y:
        powai.append([i, t])
        t = (t * t) % m
        i = i * 2

    cur = y
    mm = 1
    #print powai
    for i in powai[::-1]:
        #print i
        if cur >= i[0]:
            cur -= i[0]
            mm = (mm * i[1]) % m
            #print i, cur, mm
    return mm

ss = sys.stdin.readline().strip().split(' ')
a = long(ss[0])
b = long(ss[1])
n = long(ss[2])
x = long(ss[3])

if a == 1:
    print (x + b * n) % m
else:
    an = getpowmod(a, n)
    a1m2 = getpowmod(a-1, m-2)
    an2 = ((an - 1) * a1m2) % m
    res = (an * x + an2 * b) % m
    print res


