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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FReverseAndSwap solver = new FReverseAndSwap();
        solver.solve(1, in, out);
        out.close();
    }

    static class FReverseAndSwap {
        int[] a;
        int[] rev;
        int[] swap;
        long[] tree;

        void build(int n, int nL, int nR) {
            if (nL == nR) {
                tree[n] = a[nL];
                return;
            }
            build(2 * n + 1, nL, (nL + nR) / 2);
            build(2 * n + 2, (nL + nR) / 2 + 1, nR);
            tree[n] = tree[2 * n + 1] + tree[2 * n + 2];
        }

        long query(int n, int k, int cr, int l, int r) {
            if (r - l + 1 == (1 << k))
                return tree[n];
            cr ^= rev[k];
            int left = 2 * n + 1, right = 2 * n + 2;
            if ((swap[k] ^ cr) == 1) {
                left = 2 * n + 2;
                right = 2 * n + 1;
            }
            int m = 1 << (k - 1);
            if (r < m) {
                return query(left, k - 1, cr, l, r);
            }
            if (l >= m) {
                return query(right, k - 1, cr, l - m, r - m);
            }
            return query(left, k - 1, cr, l, m - 1) + query(right, k - 1, cr, 0, r - m);
        }

        void update(int n, int k, int cr, int i, int v) {
            if (k == 0) {
                tree[n] = v;
                return;
            }
            cr ^= rev[k];
            int left = 2 * n + 1, right = 2 * n + 2;
            if ((swap[k] ^ cr) == 1) {
                left = 2 * n + 2;
                right = 2 * n + 1;
            }
            int m = 1 << (k - 1);
            if (i < m)
                update(left, k - 1, cr, i, v);
            else
                update(right, k - 1, cr, i - m, v);
            tree[n] = tree[2 * n + 1] + tree[2 * n + 2];
        }

        public void solve(int testNumber, InputReader s, PrintWriter w) {
            int k = s.nextInt(), q = s.nextInt();
            int n = 1 << k;
            a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = s.nextInt();
            tree = new long[2 * n];
            build(0, 0, n - 1);
            rev = new int[k + 1];
            swap = new int[k + 1];
            while (q-- > 0) {
                int t = s.nextInt();
                if (t == 1)
                    update(0, k, 0, s.nextInt() - 1, s.nextInt());
                else if (t == 2)
                    rev[s.nextInt()] ^= 1;
                else if (t == 3)
                    swap[s.nextInt() + 1] ^= 1;
                else
                    w.println(query(0, k, 0, s.nextInt() - 1, s.nextInt() - 1));
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

