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 n, m, k;
int arr[100100];
long long sum;
struct Node {
  int l, r, len;
  long long lma[20], rma[20], sum;
} nde[100100 << 2];
void pushUp(int u) {
  nde[u].sum = nde[(u << 1)].sum + nde[(u << 1 | 1)].sum;
  for (int j = 0; j < 20; j++) {
    if (nde[(u << 1)].lma[j] == nde[(u << 1)].len)
      nde[u].lma[j] = nde[(u << 1)].len + nde[(u << 1 | 1)].lma[j];
    else
      nde[u].lma[j] = nde[(u << 1)].lma[j];
    if (nde[(u << 1 | 1)].rma[j] == nde[(u << 1 | 1)].len)
      nde[u].rma[j] = nde[(u << 1 | 1)].len + nde[(u << 1)].rma[j];
    else
      nde[u].rma[j] = nde[(u << 1 | 1)].rma[j];
    if (nde[(u << 1)].rma[j] != nde[(u << 1)].len &&
        nde[(u << 1 | 1)].lma[j] != nde[(u << 1 | 1)].len) {
      long long tmp = nde[(u << 1)].rma[j] + nde[(u << 1 | 1)].lma[j];
      nde[u].sum += (tmp * (tmp + 1) / 2) << j;
    }
  }
  return;
}
void build(int u, int l, int r) {
  nde[u].l = l, nde[u].r = r;
  nde[u].sum = 0;
  nde[u].len = r - l + 1;
  if (l >= r) {
    for (int j = 0; j < 20; j++) {
      nde[u].lma[j] = nde[u].rma[j] = (arr[l] >> j) & 1;
    }
    return;
  }
  int mid = (l + r) >> 1;
  build((u << 1), l, mid);
  build((u << 1 | 1), mid + 1, r);
  pushUp(u);
}
void update(int u, int p, int v) {
  if (nde[u].l >= nde[u].r) {
    nde[u].sum = 0;
    for (int j = 0; j < 20; j++) {
      nde[u].lma[j] = nde[u].rma[j] = (v >> j) & 1;
    }
    return;
  }
  if (p <= nde[(u << 1)].r)
    update((u << 1), p, v);
  else
    update((u << 1 | 1), p, v);
  pushUp(u);
}
int main() {
  int a, b;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &arr[i]);
  }
  build(1, 1, n);
  while (m--) {
    scanf("%d%d", &a, &b);
    update(1, a, b);
    long long ans = nde[1].sum;
    for (int j = 0; j < 20; j++)
      if (nde[1].lma[j] == nde[1].len) {
        long long tmp = nde[1].lma[j];
        ans += (tmp * (tmp + 1) / 2) << j;
      } else {
        long long tmp = nde[1].lma[j];
        ans += (tmp * (tmp + 1) / 2) << j;
        tmp = nde[1].rma[j];
        ans += (tmp * (tmp + 1) / 2) << j;
      }
    printf("%I64d\n", ans);
  }
  return 0;
}