Problem: Inna is fed up with jokes about female logic. So she started using binary logic instead.

Inna has an array of n elements a1[1], a1[2], ..., a1[n]. Girl likes to train in her binary logic, so she does an exercise consisting of n stages: on the first stage Inna writes out all numbers from array a1, on the i-th (i ≥ 2) stage girl writes all elements of array ai, which consists of n - i + 1 integers; the k-th integer of array ai is defined as follows: ai[k] = ai - 1[k] AND ai - 1[k + 1]. Here AND is bit-wise binary logical operation.

Dima decided to check Inna's skill. He asks Inna to change array, perform the exercise and say the sum of all <image> elements she wrote out during the current exercise.

Help Inna to answer the questions!

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 105) — size of array a1 and number of Dima's questions. Next line contains n integers a1[1], a1[2], ..., a1[n] (0 ≤ ai ≤ 105) — initial array elements.

Each of next m lines contains two integers — Dima's question description. Each question consists of two integers pi, vi (1 ≤ pi ≤ n; 0 ≤ vi ≤ 105). For this question Inna should make a1[pi] equals vi, and then perform the exercise. Please, note that changes are saved from question to question.

Output

For each question print Inna's answer on a single line.

Examples

Input

3 4
1 1 1
1 1
2 2
3 2
1 2


Output

6
4
7
12

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int A[100010], bits[100010][30];
set<pair<int, int> > rngs[30];
long long get_val(int begin, int end, int bt) {
  return 1LL * (1 << bt) * (end - begin + 1) * (end - begin + 2) / 2;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m;
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    cin >> A[i];
    for (int j = 0; j < 17; j++)
      if (A[i] & (1 << j)) bits[i][j] = 1;
  }
  long long ans = 0;
  for (int j = 0; j < 17; j++) {
    int ct = 0;
    for (int i = 1; i <= n + 1; i++) {
      if (!bits[i][j]) {
        if (ct) rngs[j].insert(make_pair(i - ct, i - 1));
        ans += 1LL * (1 << j) * (ct) * (ct + 1) / 2;
        ct = 0;
      } else
        ct++;
    }
  }
  for (int i = 0; i < m; i++) {
    int ind, val;
    cin >> ind >> val;
    for (int j = 0; j < 17; j++) {
      if (bits[ind][j] && !(val & (1 << j))) {
        auto it = rngs[j].upper_bound(make_pair(ind, 1e9));
        it--;
        int beg = it->first;
        int ed = it->second;
        ans -= get_val(beg, ed, j);
        if (beg < ind) {
          ans += get_val(beg, ind - 1, j);
          rngs[j].insert(make_pair(beg, ind - 1));
        }
        if (ed > ind) {
          ans += get_val(ind + 1, ed, j);
          rngs[j].insert(make_pair(ind + 1, ed));
        }
        rngs[j].erase(make_pair(beg, ed));
        bits[ind][j] ^= 1;
      } else if (!bits[ind][j] && (val & (1 << j))) {
        auto it = rngs[j].upper_bound(make_pair(ind, 1e9));
        int st1 = -1, ed1 = -1, st2 = -1, ed2 = -1;
        if (it != rngs[j].end()) {
          st2 = (*it).first;
          ed2 = (*it).second;
        }
        auto it2 = it;
        if (it != rngs[j].begin()) {
          it2--;
          st1 = (*it2).first;
          ed1 = (*it2).second;
        }
        if (ed1 == ind - 1 && st2 == ind + 1) {
          rngs[j].erase(make_pair(st1, ed1));
          rngs[j].erase(make_pair(st2, ed2));
          ans -= get_val(st1, ed1, j);
          ans -= get_val(st2, ed2, j);
          ans += get_val(st1, ed2, j);
          rngs[j].insert(make_pair(st1, ed2));
        } else if (ind + 1 == st2) {
          ans -= get_val(st2, ed2, j);
          ans += get_val(ind, ed2, j);
          rngs[j].erase(make_pair(st2, ed2));
          rngs[j].insert(make_pair(ind, ed2));
        } else if (ind - 1 == ed1) {
          ans -= get_val(st1, ed1, j);
          ans += get_val(st1, ind, j);
          rngs[j].erase(make_pair(st1, ed1));
          rngs[j].insert(make_pair(st1, ind));
        } else {
          rngs[j].insert(make_pair(ind, ind));
          ans += get_val(ind, ind, j);
        }
        bits[ind][j] ^= 1;
      }
    }
    cout << ans << '\n';
  }
}