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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;

public class Main {
	private static int n, k;
	private static int[] a;
	private static final int MOD = (int)1e9+7;

	public static void main(String[] args) {
		n = ini();
		k = ini();
		
		long[] dp = new long[k+1];
		
		dp[k] = 1;//exp(k, n);
		
		long ans = 0;
		ans += k;
		
		for(int i=k-1; i>=1; i--) {
			dp[i] = exp(k/i, n);
			for(int j=2*i; j<=k; j+=i) {
				dp[i]=(dp[i]-dp[j]+MOD)%MOD;
			}
			ans = (ans+i*dp[i])%MOD;
		}
		
		println(ans);
		
		out.flush();
		out.close();

	}
	
	
	private static long exp(long a, long b) {
		if (a==0) return 0;
		
		if (b==0) return 1;

		long val = exp(a, b/2);
		if (b%2==0) {
			return (val*val)%MOD;
		} else {
			long res = (val*val)%MOD;
			return (a*res)%MOD;
		}
		
	}
	

	private static int gcd(int a, int b) {
		//O(log(min(a,b)))
		if (b==0) return a;
		
		return gcd(b, a%b);
	}

	//NONPROBLEM CODE

	private static InputReader in = new InputReader(System.in);
	private static PrintWriter out = new PrintWriter(System.out);

	private static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;

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

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 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 {
				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 {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		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 String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

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

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}

	//INPUT SHORTCUTS

	private static int[] ina(int n) {
		int[] temp = new int[n];
		for (int i = 0; i < n; i++) {
			temp[i] = in.nextInt();
		}
		return temp;
	}

	private static int ini() {
		return in.nextInt();
	}

	//OTHER SHORTCUTS
	public static void sort(int[] a) {
		Arrays.sort(a);
	}

	//PRINT SHORTCUTS

	private static void println(Object... o) {
		for (Object x : o) {
			out.write(x + " ");
		}
		out.write("\n");
		out.flush();
	}

	private static void print(Object... o) {
		for (Object x : o) {
			out.write(x + " ");
		}
		out.flush();
	}

	private static void debug(Object... o) {
		for (Object x : o) {
			out.write(x + " ");
		}
		out.write("\n");
		out.flush();
	}

	private static HashMap<Integer, ArrayList<Integer>> intree(int n) {

		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();
		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < n - 1; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
			g.get(v).add(u);
		}

		return g;
	}
}
