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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class E {
    static TreeSet<Integer>[] bitLocations = new TreeSet[17];
    static int[] arr;
    static long result;

    public static void update(int sign, int length, int bit) {
        result += sign * (length * (length + 1L) / 2) * 1 << bit;
    }

    public static void remove(int i, int bit) {
        int prev = bitLocations[bit].floor(i) + 1;
        int next = bitLocations[bit].ceiling(i);
        update(-1, next - prev, bit);
        update(1, i - prev, bit);
        update(1, next - i - 1, bit);
        bitLocations[bit].add(i);
    }

    public static void add(int i, int bit) {
        int prev = bitLocations[bit].floor(i - 1) + 1;
        int next = bitLocations[bit].ceiling(i + 1);
        update(-1, i - prev, bit);
        update(-1, next - i - 1, bit);
        update(1, next - prev, bit);
        bitLocations[bit].remove(i);
    }

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer strtok;
        strtok = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(strtok.nextToken());
        int m = Integer.parseInt(strtok.nextToken());
        arr = new int[n + 1];
        result = 0;
        strtok = new StringTokenizer(in.readLine());
        for (int j = 0; j < 17; j++) {
            bitLocations[j] = new TreeSet<>();
            bitLocations[j].add(0);
            bitLocations[j].add(n + 1);
        }
        for (int i = 1; i <= n; i++) {
            arr[i] = Integer.parseInt(strtok.nextToken());
            for (int j = 0; j < 17; j++)
                if ((arr[i] & 1 << j) == 0)
                    bitLocations[j].add(i);
        }

        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < 17; j++) {
                if ((arr[i] & 1 << j) != 0) {
                    int next = bitLocations[j].ceiling(i + 1) - i;
                    result += next * (1L << j);
                }
            }
        }
        StringBuilder out = new StringBuilder();
        for (int i = 0; i < m; i++) {
            strtok = new StringTokenizer(in.readLine());
            int idx = Integer.parseInt(strtok.nextToken());
            int num = Integer.parseInt(strtok.nextToken());
            for (int j = 0; j < 17; j++) {
                if ((arr[idx] & 1 << j) != 0) {
                    remove(idx, j);
                }
            }
            arr[idx] = num;
            for (int j = 0; j < 17; j++) {
                if ((arr[idx] & 1 << j) != 0) {
                    add(idx, j);
                }
            }
            out.append(result + "\n");
        }
        System.out.print(out);
    }
}