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.io.StreamTokenizer;
public class Main {
      static long[] s=new long[1<<21];
      static long[] a=new long [1<<21];
      static int[] rev=new int[25];
      public static void build(int p,int l,int r) {
    	  int mid=(l+r)>>1;
      if (l==r) {s[p]=a[l]; return;}
      build(p*2,l,mid); build(p*2+1,mid+1,r);
      s[p]=s[p*2]+s[p*2+1];
      }
      public static void modify(int p,int l,int r,int deep,int k,long x) {
    	  if (l==r) {s[p]=x; return;}
    	  int mid=(l+r)>>1;
      if (k<=mid) modify((p*2)^rev[deep],l,mid,deep-1,k,x);
      else modify((p*2+1)^rev[deep],mid+1,r,deep-1,k,x);
      s[p]=s[p*2]+s[p*2+1];
      }
      public static long query(int p,int l,int r,int deep,int ql,int qr) {
    	  long ans=0;
    	  if (ql<=l&&r<=qr) return s[p];
    	  int mid=(l+r)>>1;
    	  if (ql<=mid) {
    		  ans+=query((p*2)^rev[deep],l,mid,deep-1,ql,qr);
    	  }
    	  if (qr>mid) ans+=query((p*2+1)^rev[deep],mid+1,r,deep-1,ql,qr);
    	  return ans;
      }
      public static void swap(int k) {
    	  rev[k+1]^=1;
      }
      public static void reve(int k) {
    	  for (int i=0;i<=k;i++) rev[i]^=1;
      }
      public static void main(String[] args) throws IOException{
    	  StreamTokenizer st = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
    	  PrintWriter out = new PrintWriter(System.out);
    	  StringBuilder sb = new StringBuilder();
    	  st.nextToken();
    	  int n=(int)st.nval; st.nextToken();
    	  int q=(int)st.nval;
    	  for (int i=0;i<=n+1;i++) rev[i]=0;
    	  for (int i=1;i<=1<<n;i++) {
    		  st.nextToken();
    		  a[i]=(int)st.nval;
    	  }
    	  build(1,1,1<<n);
    	  for (int i=1;i<=q;i++) {
    		  st.nextToken();
    		  int op=(int)st.nval;
    		  if (op==1) {
    			  st.nextToken();
        		  int x=(int)st.nval;st.nextToken();
        		  int k=(int)st.nval; modify(1,1,1<<n,n,x,k);
    		  }
    		  if (op==2) {st.nextToken();
    		  int x=(int)st.nval; reve(x);
    	  }
    		  if (op==3) {st.nextToken();
    		  int x=(int)st.nval; swap(x);
    			  }
    		  if (op==4) {st.nextToken();
    		  int l=(int)st.nval;st.nextToken();
    		  int r=(int)st.nval;
    			  long ans=query(1,1,1<<n,n,l,r);
    			  sb.append(ans+"\n");
    		  }
      }
    		out.print(sb.toString());
      		out.flush();
    }
}