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.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            long x=input.nextLong();
            long n=input.nextLong();
            ArrayList<Long> factors=primeFactors(x);
            ArrayList<ArrayList<Long>> list=new ArrayList<>();
            for(int i=0;i<factors.size();i++)
            {
                long j=1;
                ArrayList<Long> l=new ArrayList<>();
                long val=factors.get(i);
                j=j*val;
                while(j<=n && j>0)
                {
                    l.add(j);
                    if(j>n/val)
                    {
                        break;
                    }
                    j=j*val;
                }
                list.add(l);
            }
            ArrayList<ArrayList<Long>> pro=new ArrayList<>();
            for(int i=0;i<list.size();i++)
            {
                ArrayList<Long> m=new ArrayList<>();
                long p=0;
                for(int j=0;j<list.get(i).size();j++)
                {
                    long val=list.get(i).get(j);
                    p+=n/val;
                }
                if(list.get(i).size()>0)
                {
                    m.add(list.get(i).get(0));
                    m.add(p);
                    pro.add(m);
                }
            }
            long ans=1L;
            long mod=1000000007;
            for(int i=0;i<pro.size();i++)
            {
                ans=(ans%mod*power(pro.get(i).get(0),pro.get(i).get(1),mod)%mod)%mod;
            }
            out.println(ans);
        }
        out.close();
        //7246376811594199
    }
    public static ArrayList<Long> primeFactors(long n)
    {
        ArrayList<Long> list=new ArrayList<>();
        HashSet<Long> set=new HashSet<>();
        while (n%2==0)
        {
            if(!set.contains(2L))
            {
                list.add(2L);
                set.add(2L);
            }
            n /= 2;
        }
        for (long i = 3; i <= Math.sqrt(n); i+= 2)
        {
            while (n%i == 0)
            {
                if(!set.contains(i))
                {
                    list.add(i);
                    set.add(i);
                }
                n /= i;
            }
        }
        if (n > 2)
        {
            if(!set.contains(n))
            {
                set.add(n);
                list.add(n);
            }
        }
        return list;
    }
    public static long power(long a,long b,long m)
    {
        long res=1L;
        while(b>0)
        {
            if(b%2L!=0)
            {
                res=(res%m*a%m)%m;
            }
            b=b/2L;
            a=(a%m*a%m)%m;
        }
        return res;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

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

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}