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.util.*;
import java.io.*;

public class F1401 {

	static boolean[] swapped;

	static class SegmentTree {
		long[] sTree;
		int[] arr;
		int N;

		public SegmentTree(int[] in) {
			sTree = new long[in.length << 1];
			arr = in;
			build(1, in.length, 1);
			N = in.length;
		}

		public void build(int l, int r, int node) {
			if (l == r) {
				sTree[node] = arr[l - 1];
				return;
			}
			int mid = l + r >> 1;
			build(l, mid, node << 1);
			build(mid + 1, r, node << 1 | 1);
			sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
		}

		public long query(int i, int j) {
			return query(1, swapped.length - 1, 1, N, i, j);
		}

		public void update(int i, int val) {
			update(1, swapped.length - 1, 1, N, i, val);
		}

		public long query(int node, int lvl, int l, int r, int i, int j) {
			if (i <= l && r <= j) {
				return sTree[node];
			}
			if (j < l || r < i) {
				return 0;
			}
			int mid = l + r >> 1;
//			System.out.println(l + " " + r + " " + i + " " + j);
			if (!swapped[lvl]) {
				return query(node << 1, lvl - 1, l, mid, i, j) + query(node << 1 | 1, lvl - 1, mid + 1, r, i, j);
			} else {
				return query(node << 1 | 1, lvl - 1, l, mid, i, j) + query(node << 1, lvl - 1, mid + 1, r, i, j);
			}
		}

		public void update(int node, int lvl, int l, int r, int i, int val) {
			if (l == r) {
				sTree[node] = val;
				return;
			}
			int mid = l + r >> 1;
//			System.out.println(l + " " + r + " " + i);
			if ((i <= mid)) {
				update(swapped[lvl] ? (node << 1 | 1) : (node << 1), lvl - 1, l, mid, i, val);
			} else {
				update(swapped[lvl] ? (node << 1) : (node << 1 | 1), lvl - 1, mid + 1, r, i, val);
			}
			sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
		}
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int q = sc.nextInt();
		int[] in = sc.nextIntArr(1 << n);
		swapped = new boolean[n];
		SegmentTree sg = new SegmentTree(in);
//		for (int i = 1; i <= 1 << n; i++) {
//			pw.print(sg.query(i, i) + " ");
//		}
//		pw.println(Arrays.toString(sg.sTree));
		while (q-- > 0) {
			int t = sc.nextInt();
			if (t == 1) {
				sg.update(sc.nextInt(), sc.nextInt());
			} else if (t == 2) {
				int k = sc.nextInt();
				for (int i = 0; i < k; i++) {
					swapped[i] ^= true;
				}
			} else if (t == 3) {
				swapped[sc.nextInt()] ^= true;
			} else {
				pw.println(sg.query(sc.nextInt(), sc.nextInt()));
			}
//			for (int i = 1; i <= 1 << n; i++) {
//				pw.print(sg.query(i, i) + " ");
//			}
//			pw.println();
		}
//		for (int i = 1; i <= 1 << n; i++) {
//			pw.print(sg.query(i, i) + " ");
//		}
		pw.close();
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(next());
			}
			return arr;
		}

	}

}
