For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.

Constraints

* 1 ≤ m ≤ 100
* 1 ≤ n ≤ 109

Input


m n


Two integers m and n are given in a line.

Output

Print mn (mod 1,000,000,007) in a line.

Examples

Input

2 3


Output

8


Input

5 8


Output

390625
M = 1000000007

def pow(x,n)
  return 1 if n == 0
  res = pow(x*x%M,n/2)
  res *= x if n.odd?
  res
end

m,n = gets.split.map {|e|e.to_i}
puts pow(m,n)