Consider sequences \\{A_1,...,A_N\\} of length N consisting of integers between 1 and K (inclusive).

There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.

Since this sum can be enormous, print the value modulo (10^9+7).

Here \gcd(A_1, ..., A_N) denotes the greatest common divisor of A_1, ..., A_N.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq K \leq 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).

Examples

Input

3 2


Output

9


Input

3 200


Output

10813692


Input

100000 100000


Output

742202979
import java.util.*;
import java.io.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

public class Main implements Runnable
{
//    static int dx[]={-1,0,1,0};
//    static int dy[]={0,-1,0,1};
    static long mod=1000000007;
    
    public static void main(String[] args) {        
        new Thread(null, new Main(), "", 200 * 1024 * 1024).start();        
    }

    public void run() {
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);

        int n=sc.nextInt();
        int k=sc.nextInt();
        long ans=0,sb,d[]=new long[k+1];
        for (int i = k,q; 0<i; i--) {
        	q=k/i;
        	sb=power(q,n,mod);
        	for (int j = 2; j <= q; j++) {
            	sb-=d[j*i];
            	sb%=mod;
			}
            if(sb<0)sb+=mod;
        	d[i]=sb;
        	ans+=sb*i%mod;
        	ans%=mod;
		}

        out.println(ans);
     	out.flush();
    }
    
    static long power(long base, long exponent, long mod) {
		if (exponent == 0)
			return 1 % mod;
		long result = power(base, exponent >> 1, mod);
		result = result * result % mod;
		if ((exponent & 1) != 0)
			result = result * base % mod;
		return result;
	}

    static void ret(String ans) {
    	System.out.println(ans);
    	System.exit(0);
    }

    static void ret(long ans) {
    	System.out.println(ans);
    	System.exit(0);
    }
    
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
}

//class P {
//	int x,y; double d;
//	P(int  x, int y, double d) {
//	  this.x=x;
//	  this.y=y;
//	  this.d=d;
//	}
//}


//class P implements Comparable<P>{
//    int i,x,r,f;
//    P(int i,int x,int r,int f) {
//    	this.i=i;
//    	this.x=x;
//    	this.r=r;
//    	this.f=f;
//    }
//
//    public int compareTo(P p){
//    	if(-this.r+p.r==0) {
//    		return -this.x+p.x;
//    	}
//        return -this.r+p.r;
//    }
//}

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString()
    {
        while( st==null || !st.hasMoreTokens() )
			try {
				st = new StringTokenizer(x.readLine());
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        return st.nextToken();
    }
    public int nextInt()
    {
        return Integer.parseInt(nextString());
    }
    public int[] nextIntArray(int size) {
        int r[] = new int[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextInt(); 
        }
        return r;
    }
    public long[] nextLongArray(int size) {
        long r[] = new long[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextLong(); 
        }
        return r;
    }
    public char[] getCharSet() {
        return this.nextString().toCharArray();
    }    
    public long nextLong()
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}
