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
#!/usr/bin/python

import os
import sys
import itertools
import math

MOD = 10**9+7

def solve(f):
    a, b, n, x = f.read_int_list()

    if a == 1:
        return (x+b*n)%MOD
    elif a == 2:
        return (pow(a,n,MOD)*x+b*(pow(a,n,MOD)-1))%MOD
    else:
        return (pow(a,n,MOD)*x+b*(pow(a,n,MOD)-1)*modinv(a-1,MOD))%MOD


def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, y, x = egcd(b % a, a)
        return (g, x - (b / a) * y, y)

def modinv(a, m):
    g, x, y = egcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

class Reader(object):
    def __init__(self, filename=None):
        self.test_mode = filename is not None
        self.cases = 1
        self.buffer = []
        if self.test_mode:
            with open(filename) as f:
                blank_flg = False
                for line in f:
                    line = line.strip()
                    if line:
                        self.buffer.append(line)
                        blank_flg = False
                    else:
                        if not blank_flg: self.cases += 1
                        blank_flg = True

    def __readline(self):
        return self.buffer.pop(0) if self.test_mode else raw_input()

    def read_int(self):
        return int(self.__readline())
    def read_float(self):
        return float(self.__readline())
    def read_long(self):
        return long(self.__readline())
    def read_str(self):
        return self.__readline()

    def read_int_list(self):
        return [int(item) for item in self.__readline().split()]
    def read_float_list(self):
        return [float(item) for item in self.__readline().split()]
    def read_long_list(self):
        return [long(item) for item in self.__readline().split()]
    def read_str_list(self):
        return self.__readline().split()

if __name__ == '__main__':
    filename = sys.argv[1] if len(sys.argv)>1 else None
    f = Reader(filename)
    if f.test_mode:
        for c in xrange(f.cases):
            print "Case #%d"%(c+1)
            print solve(f)
    else:
        print solve(f)
