Problem:
Power

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.

Input

m n

Two integers m and n are given in a line.

Output

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

Constraints

1 ≤ m ≤ 100

1 ≤ n ≤ 109

Sample Input 1

2 3

Sample Output 1

8

Sample Input 2

5 8

Sample Output 2

390625

Solution in Ruby (judge verdict: Accepted)


def power(n, m, cache)
  return 1 if m.zero?
  return n if m == 1
  if (cache[n])
    return cache[n][m] if cache[n].has_key?(m)
  else
    cache[n] = {}
  end
  t = power(n, m / 2, cache) % 1000000007
  cache[n][m] = (m % 2 == 1 ? t * t * n : t * t) % 1000000007
end

n, m = gets.split.map(&:to_i)
cache = {}
puts power(n, m, cache)