Let's introduce some definitions that will be needed later.

Let prime(x) be the set of prime divisors of x. For example, prime(140) = \{ 2, 5, 7 \}, prime(169) = \{ 13 \}.

Let g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:

  * g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27), 
  * g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49). 



Let f(x, y) be the product of g(y, p) for all p in prime(x). For example:

  * f(30, 70) = g(70, 2) ⋅ g(70, 3) ⋅ g(70, 5) = 2^1 ⋅ 3^0 ⋅ 5^1 = 10, 
  * f(525, 63) = g(63, 3) ⋅ g(63, 5) ⋅ g(63, 7) = 3^2 ⋅ 5^0 ⋅ 7^1 = 63. 



You have integers x and n. Calculate f(x, 1) ⋅ f(x, 2) ⋅ … ⋅ f(x, n) mod{(10^{9} + 7)}.

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

Output

Print the answer.

Examples

Input


10 2


Output


2


Input


20190929 1605


Output


363165664


Input


947 987654321987654321


Output


593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class TaskC {
	private static Long MOD = 1000000007L;

	public static void main(String[] arg) {
		final FastScanner in = new FastScanner(System.in);
		final PrintWriter out = new PrintWriter(System.out);
		Solution solution = new Solution();
		long x = in.nextLong();
		long n = in.nextLong();
		out.println(solution.sol(x, n));
		out.close();
		in.close();
	}

	private static class Solution {

		public Long sol(long x, long n) {
			Long result2 = 1L;
			Set<Long> primes = prime(x);
			for (Long prime : primes) {
				long p = prime;
				while (p <= n) {
					long count = n / p;
		
					long fastPower = prime;
					while(count%2==0) {
						fastPower*=fastPower;
						fastPower%=MOD;
						count/=2;
					}
					while (count > 0) {
						while (count % 2 == 0) {
							fastPower *= fastPower;
							fastPower%=MOD;
							count /= 2;
						}
						result2 *= (fastPower%MOD);
						result2 %= MOD;
						count--;
					}
					if(p>n/prime) {
						break;
					}
					p *= prime;				
				}
			}
//            return ans.mod(BigInteger.valueOf(MOD)).longValue();
	//	System.out.printf(" %3d%n",result2);
//
//			for (long l = 1; l <= n; l++) {
////				 System.out.printf("%3d %3d%n", l, f(x, l));
//				result *= (f(x, l)%MOD);
//				result %= MOD;
//			}
//		System.out.println(result);
			return result2;
		}

		private Long f(long x, long y) {
			Set<Long> xPrime = prime(x);
			long result = 1;
			for (Long n : xPrime) {
				result *= g(y, n);
				result %= MOD;
			}
			return result;
		}

		private Long g(long x, long p) {
			long result = 1;
			while (x % (result * p) == 0) {
				result *= p;
			}
			return result;
		}

		private Set<Long> prime(long x) {
			Set<Long> result = new HashSet<>();
			while (x % 2 == 0) {
				x /= 2;
				result.add(2L);
			}
			for (long i = 3; i * i <= x; i += 2) {
				while (x % i == 0) {
					result.add(i);
					x = x / i;
				}
			}
			if (x > 1) {
				result.add(x);
			}
			return result;
		}
	}

	private static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(InputStream stream) {
			try {
				br = new BufferedReader(new InputStreamReader(stream));
			} catch (Exception e) {
				e.printStackTrace();
			}
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] readIntArr(int n) {
			int[] result = new int[n];
			for (int i = 0; i < n; i++) {
				result[i] = Integer.parseInt(next());
			}
			return result;
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}

		long nextLong() {
			return Long.parseLong(next());
		}

	}
}
