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.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * 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;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ESumOfGcdOfTuplesHard solver = new ESumOfGcdOfTuplesHard();
        solver.solve(1, in, out);
        out.close();
    }

    static class ESumOfGcdOfTuplesHard {
        public void solve(int testNumber, FastReader s, PrintWriter out) {
            int n = s.nextInt();
            int k = s.nextInt();
            long ans = 0l;
            long[] ans1 = new long[k + 1];
            int mod = 1000000007;
            for (int i = 1; i <= k; i++) {
                ans1[i] += ESumOfGcdOfTuplesHard.Maths.power(k / i, n, mod);
            }

            for (int i = k; i >= 1; i--) {
                long sum = 0l;
                for (int j = i + i; j <= k; j += i) {
                    sum = ((sum % mod) + (ans1[j] % mod)) % mod;
                }

                ans1[i] = (ans1[i] - sum + mod) % mod;
            }

            for (long i = 1; i <= k; i++) {
                ans = ((ans % mod) + ((ans1[(int) i] % mod) * (i % mod)) % mod) % mod;
            }

            out.println(ans);
        }

        private static class Maths {
            static long power(long x, long y, long p) {
                long res = 1;
                x = x % p;

                while (y > 0) {
                    if ((y & 1) == 1)
                        res = (res * x) % p;
                    y = y >> 1;
                    x = (x * x) % p;
                }
                return res;
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(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 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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

