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.util.ArrayList;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.TreeSet;
public class Solution implements Runnable
	                {
	                    static final long MAX = 464897L;
	                    static class InputReader
	                    {
	                        private InputStream stream;
	                        private byte[] buf = new byte[1024];
	                        private int curChar;
	                        private int numChars;
	                        private SpaceCharFilter filter;
	                        private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	                 
	                        public InputReader(InputStream stream)
	                        {
	                            this.stream = stream;
	                        }
	                        
	                        public int read()
	                        {
	                            if (numChars==-1) 
	                                throw new InputMismatchException();
	                            
	                            if (curChar >= numChars)
	                            {
	                                curChar = 0;
	                                try 
	                                {
	                                    numChars = stream.read(buf);
	                                }
	                                catch (IOException e)
	                                {
	                                    throw new InputMismatchException();
	                                }
	                                
	                                if(numChars <= 0)                
	                                    return -1;
	                            }
	                            return buf[curChar++];
	                        }
	                     
	                        public String nextLine()
	                        {
	                            String str = "";
	                            try
	                            {
	                                str = br.readLine();
	                            }
	                            catch (IOException e)
	                            {
	                                e.printStackTrace();
	                            }
	                            return str;
	                        }
	                        public int nextInt()
	                        {
	                            int c = read();
	                            
	                            while(isSpaceChar(c)) 
	                                c = read();
	                            
	                            int sgn = 1;
	                            
	                            if (c == '-') 
	                            {
	                                sgn = -1;
	                                c = read();
	                            }
	                            
	                            int res = 0;
	                            do 
	                            {
	                                if(c<'0'||c>'9') 
	                                    throw new InputMismatchException();
	                                res *= 10;
	                                res += c - '0';
	                                c = read();
	                            }
	                            while (!isSpaceChar(c)); 
	                            
	                            return res * sgn;
	                        }
	                        
	                        public long nextLong() 
	                        {
	                            int c = read();
	                            while (isSpaceChar(c))
	                                c = read();
	                            int sgn = 1;
	                            if (c == '-') 
	                            {
	                                sgn = -1;
	                                c = read();
	                            }
	                            long res = 0;
	                            
	                            do 
	                            {
	                                if (c < '0' || c > '9')
	                                    throw new InputMismatchException();
	                                res *= 10;
	                                res += c - '0';
	                                c = read();
	                            }
	                            while (!isSpaceChar(c));
	                                return res * sgn;
	                        }
	                        
	                        public double nextDouble() 
	                        {
	                            int c = read();
	                            while (isSpaceChar(c))
	                                c = read();
	                            int sgn = 1;
	                            if (c == '-') 
	                            {
	                                sgn = -1;
	                                c = read();
	                            }
	                            double res = 0;
	                            while (!isSpaceChar(c) && c != '.') 
	                            {
	                                if (c == 'e' || c == 'E')
	                                    return res * Math.pow(10, nextInt());
	                                if (c < '0' || c > '9')
	                                    throw new InputMismatchException();
	                                res *= 10;
	                                res += c - '0';
	                                c = read();
	                            }
	                            if (c == '.') 
	                            {
	                                c = read();
	                                double m = 1;
	                                while (!isSpaceChar(c)) 
	                                {
	                                    if (c == 'e' || c == 'E')
	                                        return res * Math.pow(10, nextInt());
	                                    if (c < '0' || c > '9')
	                                        throw new InputMismatchException();
	                                    m /= 10;
	                                    res += (c - '0') * m;
	                                    c = read();
	                                }
	                            }
	                            return res * sgn;
	                        }
	                        
	                        public String readString() 
	                        {
	                            int c = read();
	                            while (isSpaceChar(c))
	                                c = read();
	                            StringBuilder res = new StringBuilder();
	                            do 
	                            {
	                                res.appendCodePoint(c);
	                                c = read();
	                            } 
	                            while (!isSpaceChar(c));
	                            
	                            return res.toString();
	                        }
	                     
	                        public boolean isSpaceChar(int c) 
	                        {
	                            if (filter != null)
	                                return filter.isSpaceChar(c);
	                            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	                        }
	                     
	                        public String next() 
	                        {
	                            return readString();
	                        }
	                        
	                        public interface SpaceCharFilter 
	                        {
	                            public boolean isSpaceChar(int ch);
	                        }
	                    }
	                     
	                    public static void main(String args[]) throws Exception
	                    {
	                        new Thread(null, new Solution(),"Solution",1<<26).start();
	                    }   
	                    static long gcd(long a, long b) 
	                    { 
	                      if (b == 0) 
	                        return a; 
	                      return gcd(b, a % b);  
	                    } 
	                    static long lcm(long a,long b) {
	                        return (a*b)/gcd(a,b);
	                    }
	                    int maxn = 1000005;
	                    long MOD = 1000000007;
	                    long prime = 29;
	                    ArrayList<Integer> adj[];
	                    HashMap<Integer,Integer> tmap = new HashMap();
	                    int[] val;
	                 
	                	public void run() 
	                    {
	                        InputReader sc = new InputReader(System.in);
	                        PrintWriter w = new PrintWriter(System.out);
	                        int n = sc.nextInt();
	                        ArrayList<Integer> prime = new ArrayList();
	                        int count = 0;
	                        while (!(n % 2 > 0)) { 
	                            
	                            n >>= 1; 
	                        	count++;
	                        } 
	                        if(count > 0) {
	                        	prime.add(2);
	                        }
	                        for (int i = 3; i <= (int) Math.sqrt(n); i += 2) { 
	                            count = 0; 
	                            while (n % i == 0) { 
	                                count++; 
	                                n = n / i; 
	                            } 
	                            if (count > 0) { 
	                               prime.add(i);
	                            } 
	                        } 
	                        
	                        if(n > 1) {
	                        	prime.add(n);
	                        }
	                        long ans = 1;
	                        long x = sc.nextLong();
	                        for(int i = 0;i < prime.size();i++) {
	                        	long p = prime.get(i);
	                        	long ini = p;
	                        	
	                        	
	                        	while(p <= x && p > 0) {
	                        		if(p <= x/ini) {
	                        			long tr = x/p - x/(p*ini);
	                        			long jans = power(p,tr,MOD);
	                        			ans = (ans * jans) % MOD;
	                        		}else {
	                        			long tr = x/p;
	                        			long jans = power(p,tr,MOD);
	                        			ans = (ans * jans) % MOD;
	                        			break;
	                        		}
	                        		p = p * ini;
	                        	}
	                        }
	                        w.println(ans);
	                        w.close();
	                    } 
	                	boolean res(int a) {
	                		TreeSet<Integer> tset = new TreeSet();
	                		while(a != 0) {
	                			int dig = a % 10;
	                			if(tset.contains(dig)) {
	                				return false;
	                			}
	                			tset.add(dig);
	                			a = a/10;
	                		}
	                		return true;
	                	}
	                	int[] count;
	                	boolean[] color;
	                	boolean[] visited;
	                	int total;
	                	ArrayList<Integer> ans;
	                	void dfs(int a) {
	                		visited[a] = true;
	                		Iterator<Integer> it = adj[a].iterator();
	                		boolean flag = true;
	                		boolean leaf = true;
	                		while(it.hasNext()) {
	                			int x = it.next();
	                			if(!visited[x]) {
	                				leaf = false;
	                				dfs(x);
	                				if(!color[a]) {
	    	                			if(count[x] == 0) {
	    	                				flag = false;
	    	                			}
	    	                		}
	                				count[a] += count[x];
	                			}
	                			               			
	                		}
	                		if(color[a]) {
                				count[a]++;
                			}else {
                				if(flag) {
                					if(total > count[a] && a != 0) {
                						ans.add(a);
                					}
                					else if(total == count[a] && (a == 0)) {
                						ans.add(a);
                					}else if(count[a] == 0 && leaf) {
                						ans.add(a);
                					}
                				}
                			}
	                	}
	                    static long power(long a,long b,long MOD) {
                            long ans = 1;
                            a = a % MOD;
                            while(b != 0) {
                                if(b % 2 == 1) {
                                    ans = (ans * a) % MOD;
                                }
                                a = (a * a) % MOD;
                                b = b/2;
                            }
                            return ans;
                        }
	                    class Equal implements Comparable<Equal>{
	                    	Character a;
	                    	int b;
	                    	public Equal(char a,int b){
	                    		this.a = a;
	                    		this.b = b;
	                    	}
							@Override
							public int compareTo(Equal an) {
								// TODO Auto-generated method stub
								return this.a.compareTo(an.a);
								
							}
	                    }
	                    class Pair implements Comparable<Pair>{
	                        int a;
	                        int b;
	                        int c;
	                        Pair(int a,int b,int c){
	                            this.b = b;
	                            this.a = a;
	                            this.c = c;
	                        }
	                        public boolean equals(Object o) {
	                            Pair p = (Pair)o;
	                            return this.a == p.a && this.b == p.b && this.c == p.c;
	                        }
	                        public int hashCode(){
	                            return Long.hashCode(a)*27 + Long.hashCode(b)*31;
	                        }
	                        public int compareTo(Pair p) {
	                            return Long.compare(this.a,p.a);
	                        }
	                    }
	                    class Pair3 implements Comparable<Pair3>{
	                        int a;
	                        int b;
	                        int c;
	                        Pair3(int a,int b,int c){
	                            this.b = b;
	                            this.a = a;
	                            this.c = c;
	                        }
	                        public boolean equals(Object o) {
	                            Pair3 p = (Pair3)o;
	                            return this.a == p.a && this.b == p.b && this.c == p.c;
	                        }
	                        public int hashCode(){
	                            return Long.hashCode(a)*27 + Long.hashCode(b)*31;
	                        }
	                        public int compareTo(Pair3 p) {
	                            return Long.compare(this.b,p.b);
	                        }
	                    }
	                    class Pair2 implements Comparable<Pair2>{
	                        int a;
	                        int b;
	                        int c;
	                        Pair2(int a,int b,int c){
	                            this.b = b;
	                            this.a = a;
	                            this.c = c;
	                        }
	                        public boolean equals(Object o) {
	                            Pair2 p = (Pair2)o;
	                            return this.a == p.a && this.b == p.b && this.c == p.c;
	                        }
	                        public int hashCode(){
	                            return Long.hashCode(a)*27 + Long.hashCode(b)*31 + Long.hashCode(c)*3;
	                        }
	                        public int compareTo(Pair2 p) {
	                            return Long.compare(p.a,this.a);
	                        }
	                    }
	                }