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;
const int MAXN = 100000;
const int MAXM = 100000;
const int MAXFLOORLOGA = 17;
bool digits[MAXFLOORLOGA][MAXN + 2];
map<int, int> groups[MAXFLOORLOGA];
long long part_res[MAXFLOORLOGA];
long long f(long long n) { return n * (n + 1) / 2; }
map<int, int>::iterator find_prev(int dnum, int ind) {
  map<int, int>::iterator iter;
  iter = groups[dnum].upper_bound(ind);
  return --iter;
}
void update(int dnum, int ind, bool d) {
  ind += 1;
  if (d == digits[dnum][ind]) return;
  bool l = digits[dnum][ind - 1];
  bool r = digits[dnum][ind + 1];
  int lcnt, rcnt;
  int lind, rind;
  digits[dnum][ind] = d;
  if (d) {
    if (l && r) {
      lcnt = find_prev(dnum, ind - 1)->second;
      rcnt = find_prev(dnum, ind + 1)->second;
      part_res[dnum] -= f(lcnt) + f(rcnt);
      groups[dnum].erase(ind + 1);
      find_prev(dnum, ind - 1)->second = lcnt + rcnt + 1;
      part_res[dnum] += f(lcnt + rcnt + 1);
    } else if (l) {
      lcnt = find_prev(dnum, ind - 1)->second;
      part_res[dnum] += lcnt + 1;
      find_prev(dnum, ind - 1)->second += 1;
    } else if (r) {
      rcnt = find_prev(dnum, ind + 1)->second;
      groups[dnum].erase(ind + 1);
      groups[dnum][ind] = rcnt + 1;
      part_res[dnum] += rcnt + 1;
    } else {
      groups[dnum][ind] = 1;
      part_res[dnum] += 1;
    }
  } else {
    if (l & r) {
      lind = find_prev(dnum, ind - 1)->first;
      lcnt = groups[dnum][lind];
      part_res[dnum] -= f(lcnt);
      groups[dnum][lind] = ind - lind;
      groups[dnum][ind + 1] = lind + lcnt - ind - 1;
      part_res[dnum] += f(groups[dnum][lind]) + f(groups[dnum][ind + 1]);
    } else if (l) {
      lind = find_prev(dnum, ind - 1)->first;
      lcnt = groups[dnum][lind];
      part_res[dnum] -= lcnt;
      groups[dnum][lind] -= 1;
    } else if (r) {
      part_res[dnum] -= groups[dnum][ind];
      groups[dnum][ind + 1] = groups[dnum][ind] - 1;
      groups[dnum].erase(ind);
    } else {
      part_res[dnum] -= 1;
      groups[dnum].erase(ind);
    }
  }
}
long long get_res() {
  long long r = 0;
  for (int i = 0; i < MAXFLOORLOGA; ++i) r += part_res[i] << i;
  return r;
}
int N, M;
void debug_print() {
  for (int dnum = 0; dnum < 4; ++dnum) {
    cout << dnum << ": ";
    for (int i = 0; i < N + 2; ++i) cout << digits[dnum][i] << " ";
    cout << " [" << part_res[dnum] << "]" << endl;
    for (map<int, int>::iterator it = groups[dnum].begin();
         it != groups[dnum].end(); ++it)
      cout << it->first << " " << it->second << endl;
    cout << endl << endl;
  }
}
int main() {
  memset(digits, 0, sizeof(digits));
  memset(part_res, 0, sizeof(part_res));
  for (int i = 0; i < MAXFLOORLOGA; ++i) {
    part_res[i] = 0;
  }
  scanf("%d %d", &N, &M);
  for (int i = 0; i < N; ++i) {
    int ai;
    scanf("%d", &ai);
    for (int dnum = 0; dnum < MAXFLOORLOGA; ++dnum)
      update(dnum, i, ai & (1 << dnum));
  }
  for (int i = 0; i < M; ++i) {
    int ind, bi;
    scanf("%d %d", &ind, &bi);
    for (int dnum = 0; dnum < MAXFLOORLOGA; ++dnum)
      update(dnum, ind - 1, bi & (1 << dnum));
    cout << get_res() << endl;
  }
  return 0;
}