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.*;
import java.util.*;

/*
polyakoff
*/

public class Main {

    static FastReader in;
    static PrintWriter out;
    static Random rand = new Random();
    static final int oo = (int) 2e9;
    static final long OO = (long) 4e18;
    static final int MOD = (int) 1e9 + 7;

    static class SegTree {
        class Node {
            long sum;
            int rev;
            Node left, right;

            Node() {
            }
        }
        int size;
        Node root;

        void push(Node t, int tl, int tr) {
            if ((t.rev & (tr - tl + 1)) != 0) {
                Node temp = t.left;
                t.left = t.right;
                t.right = temp;
                t.rev ^= ((tr - tl + 1) >> 1);
            }
            t.left.rev ^= t.rev;
            t.right.rev ^= t.rev;
            t.rev = 0;
        }
        void pull(Node t) {
            t.sum = t.left.sum + t.right.sum;
        }

        Node build(int tl, int tr, int[] arr) {
            Node t = new Node();
            if (tl == tr) {
                t.sum = arr[tl];
            } else {
                int tm = (tl + tr) / 2;
                t.left = build(tl, tm, arr);
                t.right = build(tm + 1, tr, arr);
                pull(t);
            }
            return t;
        }
        void upd(Node t, int tl, int tr, int ind, int val) {
            if (tl == tr) {
                t.sum = val;
            } else {
                int tm = (tl + tr) / 2;
                push(t, tl, tr);
                if (ind <= tm)
                    upd(t.left, tl, tm, ind, val);
                else
                    upd(t.right, tm + 1, tr, ind, val);
                pull(t);
            }
        }
        long sumOn(Node t, int tl, int tr, int l, int r) {
            if (l <= tl && tr <= r) {
                return t.sum;
            } else {
                int tm = (tl + tr) / 2;
                push(t, tl, tr);
                if (r <= tm)
                    return sumOn(t.left, tl, tm, l, r);
                else if (l > tm)
                    return sumOn(t.right, tm + 1, tr, l, r);
                else
                    return sumOn(t.left, tl, tm, l, tm) +
                            sumOn(t.right, tm + 1, tr, tm + 1, r);
            }
        }

        void build(int[] arr) {
            size = arr.length;
            root = build(0, size - 1, arr);
        }
        void upd(int ind, int val) {
            upd(root, 0, size - 1, ind, val);
        }
        void rev(int k) {
            root.rev ^= (1 << k);
        }
        long sumOn(int l, int r) {
            return sumOn(root, 0, size - 1, l, r);
        }
    }


    static void solve() {
        int n = in.nextInt();
        int q = in.nextInt();

        int[] a = new int[1 << n];
        for (int i = 0; i < (1 << n); i++)
            a[i] = in.nextInt();

        SegTree st = new SegTree();
        st.build(a);

        for (int i = 0; i < q; i++) {
            int type = in.nextInt();
            if (type == 1) {
                int x = in.nextInt() - 1;
                int k = in.nextInt();
                st.upd(x, k);
            } else if (type == 2) {
                int k = in.nextInt();
                st.rev(k);
            } else if (type == 3) {
                int k = in.nextInt();
                st.rev(k + 1);
                st.rev(k);
            } else if (type == 4) {
                int l = in.nextInt() - 1;
                int r = in.nextInt() - 1;
                out.println(st.sumOn(l, r));
            }
        }


    }

    public static void main(String[] args) throws FileNotFoundException {
        in = new FastReader(System.in);
//        in = new FastReader(new FileInputStream("sometext.txt"));
        out = new PrintWriter(System.out);
//        out = new PrintWriter(new FileOutputStream("output.txt"));

        int T = 1;
//        T = in.nextInt();
        while (T-- > 0)
            solve();

//        Thread thread = new Thread(null, () -> {
//            solve();
//        }, "Main", 1 << 28);
//        thread.start();
//        try {
//            thread.join();
//        } catch (InterruptedException e) {
//            e.printStackTrace();
//        }

//        out.flush();
        out.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        Integer nextInt() {
            return Integer.parseInt(next());
        }

        Long nextLong() {
            return Long.parseLong(next());
        }

        Double nextDouble() {
            return Double.parseDouble(next());
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

        String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }
    }

    static void dbg(Object... args) {
        for (Object arg : args)
            out.print(" " + arg);
        out.flush();
    }

}