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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Hola solver = new Hola();
        solver.solve(1, in, out);
        out.close();
    }

    static class Hola {
        PrintWriter out;
        InputReader in;
        long mod = (long)1e9 + 7;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.out = out;
            this.in = in;
            int n = ni(), k = ni();
            int[] cnt = new int[k + 1];
            int i = 0, j = 0;
            for(i = 1; i <= k; i++){
                for(j = i ; j <= k; j += i)
                    cnt[i]++;
            }
            long[] dp = new long[k + 1];
            for(i = k; i >= 1; i--){
                dp[i] = modPow(cnt[i], n);
                for(j = i + i; j <= k; j += i){
                    dp[i] -= dp[j];
                    dp[i] += mod;
                    dp[i] %= mod;
                }
            }
            long ans = 0;
            for(i = 1; i <= k; i++){
                ans += ((long)i * dp[i]) % mod;
                ans %= mod;
            }
            pn(ans);
        }
        int gcd(int a, int b)
        {
            if (a == 0)
                return b;

            return gcd(b%a, a);
        }
        long mul(long a,long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            a*=b;
            if(a>=mod)a%=mod;
            return a;
        }
        long modPow(long a, long p){
            long o = 1;
            while(p>0){
                if((p&1)==1)o = mul(o,a);
                a = mul(a,a);
                p>>=1;
            }
            return o;
        }
        final Comparator<Tuple> com = new Comparator<Tuple>() {
            @Override
            public int compare(Tuple t1, Tuple t2) {
                if(t1.x != t2.x)
                    return Long.compare(t1.x, t2.x);
                else
                    return Long.compare(t2.y, t1.y);
            }
        };
        class Tuple{
            int x, y;
            Tuple(int x, int y){
                this.x = x;
                this.y = y;
            }
        }
        int ni() {
            return in.nextInt();
        }
        long nl() {
            return in.nextLong();
        }
        void pn(Object o) {
            out.println(o);
        }
        void p(Object o) {
            out.print(o);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}
