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, n = gets.split.map &:to_i
$t = 1000000007

def pow(m, n)
  m = m % $t
  if n == 0
    1
  elsif n.even?
    pow(m * m, n / 2)
  else
    pow(m * m, n / 2) * m
  end
end

puts pow(m, n)