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, q, illiliiililliiiiill[30][100002], v[100002];
long long iiililililiillilliliiliil[30];
void liliiiiiiiiiilllilililiililili(int, int);
void liliiiiiiiiiilllilililiililili(int, int, int);
int llllliiiiillilillilililillliiil(int, int);
long long lilililiiiilillllllllllll();
bool lililllliliiiliiilillllliiiiii(int, int);
int iiiiiililliillllliiilllllllllll(int, int);
int ililiiiliilllliililiiiilililili(int, int);
int main() {
  cin >> n >> q;
  for (int i = 1, x; i <= n; i++) {
    cin >> x;
    liliiiiiiiiiilllilililiililili(i, x);
  }
  for (int a, b; q; q--) {
    cin >> a >> b;
    liliiiiiiiiiilllilililiililili(a, b);
    cout << lilililiiiilillllllllllll() << '\n';
  }
  return 0;
}
void liliiiiiiiiiilllilililiililili(
    int iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, int x) {
  for (int i = 0;
       (1 << i) <= max(x, v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii]);
       i++)
    if (((1 << i) & x) !=
        ((1 << i) & v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii])) {
      if ((1 << i) & x) {
        if (!lililllliliiiliiilillllliiiiii(
                i, v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1]) &&
            !lililllliliiiliiilillllliiiiii(
                i, v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1])) {
          iiililililiillilliliiliil[i]++;
        } else if (!lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1]) &&
                   lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1])) {
          int dr = iiiiiililliillllliiilllllllllll(
              iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i);
          int iliiililillilil =
              dr - iiiiiiillllllllllllllllllilililiiiiiiilliiiiii;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil++;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
        } else if (lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1]) &&
                   !lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1])) {
          int st = ililiiiliilllliililiiiilililili(
              iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i);
          int iliiililillilil =
              iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - st;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil++;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
        } else {
          int st = ililiiiliilllliililiiiilililili(
                  iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i),
              dr = iiiiiililliillllliiilllllllllll(
                  iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i);
          int iliiililillilil =
              dr - iiiiiiillllllllllllllllllilililiiiiiiilliiiiii;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil = iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - st;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil = dr - st + 1;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
        }
      } else {
        if (!lililllliliiiliiilillllliiiiii(
                i, v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1]) &&
            !lililllliliiiliiilillllliiiiii(
                i, v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1])) {
          iiililililiillilliliiliil[i]--;
        } else if (!lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1]) &&
                   lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1])) {
          int dr = iiiiiililliillllliiilllllllllll(
              iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i);
          int iliiililillilil =
              dr - iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil--;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
        } else if (lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1]) &&
                   !lililllliliiiliiilillllliiiiii(
                       i,
                       v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1])) {
          int st = ililiiiliilllliililiiiilililili(
              iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i);
          int iliiililillilil =
              iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - st + 1;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil--;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
        } else {
          int st = ililiiiliilllliililiiiilililili(
                  iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i),
              dr = iiiiiililliillllliiilllllllllll(
                  iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i);
          int iliiililillilil = dr - st + 1;
          iiililililiillilliliiliil[i] -=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil = dr - iiiiiiillllllllllllllllllilililiiiiiiilliiiiii;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
          iliiililillilil = iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - st;
          iiililililiillilliliiliil[i] +=
              1ll * iliiililillilil * (iliiililillilil + 1) / 2;
        }
      }
      liliiiiiiiiiilllilililiililili(
          iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, i,
          (!!((1 << i) & x)) -
              (!!((1 << i) &
                  v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii])));
    }
  v[iiiiiiillllllllllllllllllilililiiiiiiilliiiiii] = x;
}
void liliiiiiiiiiilllilililiililili(
    int iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, int x, int val) {
  while (iiiiiiillllllllllllllllllilililiiiiiiilliiiiii <= n)
    illiliiililliiiiill[x][iiiiiiillllllllllllllllllilililiiiiiiilliiiiii] +=
        val,
        iiiiiiillllllllllllllllllilililiiiiiiilliiiiii +=
        iiiiiiillllllllllllllllllilililiiiiiiilliiiiii &
        -iiiiiiillllllllllllllllllilililiiiiiiilliiiiii;
}
int llllliiiiillilillilililillliiil(
    int iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, int x) {
  int ililiiiiiiliiililililllllllilililililillli = 0;
  while (iiiiiiillllllllllllllllllilililiiiiiiilliiiiii > 0)
    ililiiiiiiliiililililllllllilililililillli +=
        illiliiililliiiiill[x][iiiiiiillllllllllllllllllilililiiiiiiilliiiiii],
        iiiiiiillllllllllllllllllilililiiiiiiilliiiiii -=
        iiiiiiillllllllllllllllllilililiiiiiiilliiiiii &
        -iiiiiiillllllllllllllllllilililiiiiiiilliiiiii;
  return ililiiiiiiliiililililllllllilililililillli;
}
bool lililllliliiiliiilillllliiiiii(
    int iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, int x) {
  return (!!((1 << iiiiiiillllllllllllllllllilililiiiiiiilliiiiii) & x));
}
long long lilililiiiilillllllllllll() {
  long long ililiiiiiiliiililililllllllilililililillli = 0;
  for (int i = 0; i <= 29; i++)
    ililiiiiiiliiililililllllllilililililillli +=
        1ll * iiililililiillilliliiliil[i] * (1 << i);
  return ililiiiiiiliiililililllllllilililililillli;
}
int iiiiiililliillllliiilllllllllll(
    int iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, int x) {
  int st = iiiiiiillllllllllllllllllilililiiiiiiilliiiiii + 1, dr = n, p,
      fsum = llllliiiiillilillilililillliiil(
          iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, x);
  while (st <= dr) {
    int llllllllliliiililiiiliilliiiiilliillilil = (st + dr) / 2;
    int msum = llllliiiiillilillilililillliiil(
        llllllllliliiililiiiliilliiiiilliillilil, x);
    if (msum - fsum == llllllllliliiililiiiliilliiiiilliillilil -
                           iiiiiiillllllllllllllllllilililiiiiiiilliiiiii)
      st = llllllllliliiililiiiliilliiiiilliillilil + 1,
      p = llllllllliliiililiiiliilliiiiilliillilil;
    else
      dr = llllllllliliiililiiiliilliiiiilliillilil - 1;
  }
  return p;
}
int ililiiiliilllliililiiiilililili(
    int iiiiiiillllllllllllllllllilililiiiiiiilliiiiii, int x) {
  int st = 1, dr = iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1, p,
      fsum = llllliiiiillilillilililillliiil(
          iiiiiiillllllllllllllllllilililiiiiiiilliiiiii - 1, x);
  while (st <= dr) {
    int llllllllliliiililiiiliilliiiiilliillilil = (st + dr) / 2;
    int msum = llllliiiiillilillilililillliiil(
        llllllllliliiililiiiliilliiiiilliillilil - 1, x);
    if (iiiiiiillllllllllllllllllilililiiiiiiilliiiiii -
            llllllllliliiililiiiliilliiiiilliillilil ==
        fsum - msum)
      dr = llllllllliliiililiiiliilliiiiilliillilil - 1,
      p = llllllllliliiililiiiliilliiiiilliillilil;
    else
      st = llllllllliliiililiiiliilliiiiilliillilil + 1;
  }
  return p;
}