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 MAX_BITS = 18;
const int MAXN = (int)1e5 + 5;
const int INF = (int)1e9;
struct Range {
  int l;
  int r;
  Range() {}
  Range(int l, int r) : l(l), r(r) {}
};
int a[MAXN];
set<Range> s[MAX_BITS];
bool operator<(const Range& a, const Range& b) {
  return a.r < b.r || (a.r == b.r && a.l < b.l);
}
long long get_ans(int len, int shift) {
  return ((1LL << shift) * len * (len + 1)) / 2;
}
int main(void) {
  int n, m;
  scanf(" %d %d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf(" %d", &a[i]);
  }
  long long ans = 0;
  for (int shift = 0; shift < MAX_BITS; shift++) {
    int start = -1;
    for (int i = 1; i <= n; i++) {
      if ((a[i] >> shift) & 1) {
        if (start == -1) {
          start = i;
        }
      } else if (start != -1) {
        s[shift].insert(Range(start, i - 1));
        ans += get_ans(i - start, shift);
        start = -1;
      }
    }
    if (start != -1) {
      s[shift].insert(Range(start, n));
      ans += get_ans(n - start + 1, shift);
    }
  }
  while (m--) {
    int p, v;
    scanf(" %d %d", &p, &v);
    for (int shift = 0; shift < MAX_BITS; shift++) {
      auto it = s[shift].lower_bound(Range(-INF, p));
      if (it != s[shift].end() && it->l <= p && p <= it->r) {
        if (((v >> shift) & 1) == 0) {
          int len = it->r - it->l + 1;
          ans -= get_ans(len, shift);
          if (len != 1) {
            if (it->l <= p - 1) {
              s[shift].insert(Range(it->l, p - 1));
              ans += get_ans(p - it->l, shift);
            }
            if (p + 1 <= it->r) {
              s[shift].insert(Range(p + 1, it->r));
              ans += get_ans(it->r - p, shift);
            }
          }
          s[shift].erase(it);
        }
      } else {
        if ((v >> shift) & 1) {
          if (it != s[shift].end() && it->l == p + 1) {
            int len = it->r - it->l + 1;
            ans -= get_ans(len, shift);
            ans += get_ans(len + 1, shift);
            s[shift].insert(Range(p, it->r));
            s[shift].erase(it);
          } else {
            s[shift].insert(Range(p, p));
            ans += get_ans(1, shift);
          }
          it = s[shift].lower_bound(Range(-INF, p));
          if (it != s[shift].begin()) {
            auto prev = it;
            prev--;
            if (prev->r == p - 1) {
              ans -= get_ans(prev->r - prev->l + 1, shift);
              ans -= get_ans(it->r - it->l + 1, shift);
              ans += get_ans(it->r - prev->l + 1, shift);
              s[shift].insert(Range(prev->l, it->r));
              s[shift].erase(it);
              s[shift].erase(prev);
            }
          }
        }
      }
    }
    printf("%lld\n", ans);
  }
  return 0;
}