Problem: Let's call an array a of size n coprime iff gcd(a1, a2, ..., an) = 1, where gcd is the greatest common divisor of the arguments.

You are given two numbers n and k. For each i (1 ≤ i ≤ k) you have to determine the number of coprime arrays a of size n such that for every j (1 ≤ j ≤ n) 1 ≤ aj ≤ i. Since the answers can be very large, you have to calculate them modulo 109 + 7.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 2·106) — the size of the desired arrays and the maximum upper bound on elements, respectively.

Output

Since printing 2·106 numbers may take a lot of time, you have to output the answer in such a way:

Let bi be the number of coprime arrays with elements in range [1, i], taken modulo 109 + 7. You have to print <image>, taken modulo 109 + 7. Here <image> denotes bitwise xor operation (^ in C++ or Java, xor in Pascal).

Examples

Input

3 4


Output

82


Input

2000000 8


Output

339310063

Note

Explanation of the example:

Since the number of coprime arrays is large, we will list the arrays that are non-coprime, but contain only elements in range [1, i]:

For i = 1, the only array is coprime. b1 = 1.

For i = 2, array [2, 2, 2] is not coprime. b2 = 7.

For i = 3, arrays [2, 2, 2] and [3, 3, 3] are not coprime. b3 = 25.

For i = 4, arrays [2, 2, 2], [3, 3, 3], [2, 2, 4], [2, 4, 2], [2, 4, 4], [4, 2, 2], [4, 2, 4], [4, 4, 2] and [4, 4, 4] are not coprime. b4 = 55.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7, MAXN = 2e6 + 10;
inline int sum(int a, int b) {
  if (a + b >= MOD) return a + b - MOD;
  if (a + b < 0) return a + b + MOD;
  return a + b;
}
inline void add(int &a, int b) { a = sum(a, b); }
inline int mul(int a, int b) { return (long long)a * (long long)b % MOD; }
int n, k, sito[MAXN], DP[MAXN], pot_mem[MAXN];
int potn(int a) {
  if (pot_mem[a] != -1) return pot_mem[a];
  int x = n, res = 1, orig = a;
  while (x > 0) {
    if (x & 1) res = mul(res, a);
    a = mul(a, a);
    x >>= 1;
  }
  return pot_mem[orig] = res;
}
int main() {
  cin >> n >> k;
  memset(pot_mem, -1, sizeof pot_mem);
  sito[1] = 1;
  for (int i = 2; i < MAXN; i++) {
    if (sito[i] != 0) continue;
    sito[i] = i;
    for (int j = i; j < MAXN; j += i) {
      if (sito[j] != 0) continue;
      sito[j] = i;
    }
  }
  DP[1] = 1;
  int ans = 0;
  for (int i = 2; i <= k; i++) {
    add(DP[i], potn(i));
    add(DP[i], -potn(i - 1));
    add(DP[i], DP[i - 1]);
    deque<pair<int, int> > fakt;
    deque<int> djel;
    fakt.push_back(make_pair(1, 1));
    for (int d = i; sito[d] != 1; d = d / sito[d]) {
      if (fakt.rbegin()->first != sito[d])
        fakt.push_back(make_pair(sito[d], 0));
      fakt.rbegin()->second++;
    }
    fakt.pop_front();
    djel.push_back(1);
    for (pair<int, int> cur : fakt) {
      int sz = djel.size();
      for (int j = 0; j < sz; j++) {
        int cn = 1;
        for (int l = 0; l < cur.second; l++) {
          cn *= cur.first;
          djel.push_back(djel[j] * cn);
        }
      }
    }
    djel.pop_front();
    for (int cur : djel) {
      add(DP[i], -DP[i / cur]);
      add(DP[i], DP[(i - 1) / cur]);
    }
    add(ans, DP[i] ^ i);
  }
  cout << ans << endl;
  return 0;
}