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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author htvu
 */
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 {
    private boolean[] swapped;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt(), Q = in.nextInt();
      int[] a = in.readArray(1 << n);
      swapped = new boolean[1 << n];

      SegTree st = new SegTree(0, (1 << n) - 1, n, a);
      for (int run = 0; run < Q; run++) {
        int q = in.nextInt();
        if (q == 1) { // update
          int idx = in.nextInt() - 1, val = in.nextInt();
          st.update(idx, val);
        } else if (q == 2) { // reverse
          int k = in.nextInt();
          for (int i = 0; i <= k; ++i)
            swapped[i] ^= true;
        } else if (q == 3) { // swap
          int k = in.nextInt();
          swapped[k + 1] ^= true;
        } else { // query
          int l = in.nextInt() - 1, r = in.nextInt() - 1;
          out.println(st.rangeSum(l, r));
        }
//      st.printTree(); System.out.println();
      }
    }

    private class SegTree {
      long sum = 0;
      int level;
      SegTree left;
      SegTree right;

      SegTree getLeft() {
        return swapped[level] ? right : left;
      }

      SegTree getRight() {
        return swapped[level] ? left : right;
      }

      SegTree(int leftmost, int rightmost, int level, int[] a) {
        this.level = level;
        if (leftmost == rightmost) {
          this.sum = a[leftmost];
          return;
        }
        int mid = leftmost + (rightmost - leftmost) / 2;
        left = new SegTree(leftmost, mid, level - 1, a);
        right = new SegTree(mid + 1, rightmost, level - 1, a);
        recalc();
      }

      void recalc() {
        sum = getLeft().sum + getRight().sum;
      }

      void update(int idx, int newVal) {
        if (level == 0) {
          sum = newVal;
          return;
        }

        if (idx < 1 << (level - 1)) {
          getLeft().update(idx, newVal);
        } else {
          getRight().update(idx - (1 << (level - 1)), newVal);
        }
        recalc();
      }

      long rangeSum(int l, int r) {
        if (l <= 0 && r >= (1 << level) - 1)
          return sum;
        if (r < 0 || l >= 1 << level)
          return 0;
        return getLeft().rangeSum(l, r) + getRight().rangeSum(l - (1 << (level - 1)), r - (1 << (level - 1)));
      }

    }

  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

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

    public int[] readArray(int n) {
      int[] res = new int[n];
      for (int i = 0; i < n; ++i)
        res[i] = nextInt();
      return res;
    }

  }
}

