You are given an array a of length 2^n. You should process q queries on it. Each query has one of the following 4 types: 

  1. Replace(x, k) — change a_x to k; 
  2. Reverse(k) — reverse each subarray [(i-1) ⋅ 2^k+1, i ⋅ 2^k] for all i (i ≥ 1); 
  3. Swap(k) — swap subarrays [(2i-2) ⋅ 2^k+1, (2i-1) ⋅ 2^k] and [(2i-1) ⋅ 2^k+1, 2i ⋅ 2^k] for all i (i ≥ 1); 
  4. Sum(l, r) — print the sum of the elements of subarray [l, r]. 



Write a program that can quickly process given queries.

Input

The first line contains two integers n, q (0 ≤ n ≤ 18; 1 ≤ q ≤ 10^5) — the length of array a and the number of queries.

The second line contains 2^n integers a_1, a_2, …, a_{2^n} (0 ≤ a_i ≤ 10^9).

Next q lines contains queries — one per line. Each query has one of 4 types: 

  * "1 x k" (1 ≤ x ≤ 2^n; 0 ≤ k ≤ 10^9) — Replace(x, k); 
  * "2 k" (0 ≤ k ≤ n) — Reverse(k); 
  * "3 k" (0 ≤ k < n) — Swap(k); 
  * "4 l r" (1 ≤ l ≤ r ≤ 2^n) — Sum(l, r). 



It is guaranteed that there is at least one Sum query.

Output

Print the answer for each Sum query.

Examples

Input


2 3
7 4 9 9
1 2 8
3 1
4 2 4


Output


24


Input


3 8
7 0 8 8 7 1 5 2
4 3 7
2 1
3 2
4 1 6
2 3
1 5 16
4 8 8
3 0


Output


29
22
1

Note

In the first sample, initially, the array a is equal to \{7,4,9,9\}.

After processing the first query. the array a becomes \{7,8,9,9\}.

After processing the second query, the array a_i becomes \{9,9,7,8\}

Therefore, the answer to the third query is 9+7+8=24.

In the second sample, initially, the array a is equal to \{7,0,8,8,7,1,5,2\}. What happens next is: 

  1. Sum(3, 7) → 8 + 8 + 7 + 1 + 5 = 29; 
  2. Reverse(1) → \{0,7,8,8,1,7,2,5\}; 
  3. Swap(2) → \{1,7,2,5,0,7,8,8\}; 
  4. Sum(1, 6) → 1 + 7 + 2 + 5 + 0 + 7 = 22; 
  5. Reverse(3) → \{8,8,7,0,5,2,7,1\}; 
  6. Replace(5, 16) → \{8,8,7,0,16,2,7,1\}; 
  7. Sum(8, 8) → 1; 
  8. Swap(0) → \{8,8,0,7,2,16,1,7\}. 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Task6 {
    boolean[] ancestorsAreSwapped;
    Node root;

    private static class Node {
        long sum;
        Node left;
        Node right;
    }

    public static void main(String[] args) throws IOException {
        new Task6().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        StringTokenizer tokenizer = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(tokenizer.nextToken());
        int q = Integer.parseInt(tokenizer.nextToken());
        tokenizer = new StringTokenizer(f.readLine());
        int[] ar = new int[1 << n];
        for (int i = 0; i < ar.length; i++) ar[i] = Integer.parseInt(tokenizer.nextToken());
        root = new Node();
        makeChildren(root, n, ar, 0);
        ancestorsAreSwapped = new boolean[n + 1];

        for (int q1 = 0; q1 < q; q1++) {
            tokenizer = new StringTokenizer(f.readLine());
            int query = Integer.parseInt(tokenizer.nextToken());
            if (query == 1) {
                replace(root, 0, Integer.parseInt(tokenizer.nextToken()) - 1, Integer.parseInt(tokenizer.nextToken()), n);
            } else if (query == 2) {
                int k = Integer.parseInt(tokenizer.nextToken());
                for (int i = k; i >= 0; i--) {
                    ancestorsAreSwapped[i] = !ancestorsAreSwapped[i];
                }
            } else if (query == 3) {
                int k = Integer.parseInt(tokenizer.nextToken());
                ancestorsAreSwapped[k + 1] = !ancestorsAreSwapped[k + 1];
            } else {
                int l = Integer.parseInt(tokenizer.nextToken()) - 1;
                int r = Integer.parseInt(tokenizer.nextToken()) - 1;
                out.println(getSum(root, n, l, r, 0, (1 << n) - 1));
            }
        }

        out.close();
    }

    private long getSum(Node node, int n, int from, int to, int a, int b) {
        //System.out.println(a + " " + b + " " + ancestorsAreSwapped[n]) ;
        if (from <= a && b <= to) {
            //System.out.println(a + " " + b ) ;
            return node.sum;
        }

        Node left;
        Node right;
        if (ancestorsAreSwapped[n]) {
            left = node.right;
            right = node.left;
        } else {
            left = node.left;
            right = node.right;
        }

        int mid = (a + b) / 2;
        long sum = 0;

        if (from <= mid) sum += getSum(left, n - 1, from, to, a, mid );
        if (to > mid) sum += getSum(right,n - 1, from, to, mid + 1, b);

        return sum;
    }

    private long makeChildren(Node node, int n, int[] ar, int index) {
        if (n == 0) {
            node.sum = ar[index];
            return node.sum;
        }

        node.left = new Node();
        node.sum = makeChildren(node.left, n - 1, ar, index);
        node.right = new Node();
        node.sum += makeChildren(node.right, n - 1, ar, index + (1 << (n - 1)));

        return node.sum;
    }

    private void replace(Node node, int index, int targetIndex, int num, int n) {
        if (n == 0) {
            node.sum = num;
            return;
        }

        Node left;
        Node right;
        if (ancestorsAreSwapped[n]) {
            left = node.right;
            right = node.left;
        } else {
            left = node.left;
            right = node.right;
        }

        if (targetIndex >= (index + (1 << (n - 1)))) {
            replace(right, index + (1 << (n - 1)), targetIndex, num, n - 1);
        } else {
            replace(left, index, targetIndex, num, n - 1);
        }

        node.sum = node.left.sum + node.right.sum;
    }
}
