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\}. 
#include <bits/stdc++.h>
using namespace std;
const int SZ = (1 << 19) + 5;
int ln, n, q, ar[(1 << 18) + 5];
long long seg[SZ];
bool rev[18];
void bld(int idx, int L, int R) {
  if (L == R) {
    seg[idx] = ar[L];
  } else if (L < R) {
    int M = L + R >> 1;
    bld(2 * idx, L, M);
    bld(2 * idx + 1, M + 1, R);
    seg[idx] = seg[2 * idx] + seg[2 * idx + 1];
  }
}
void upd(int d, int idx, int L, int R, int x, int v) {
  if (L == x && x == R) {
    seg[idx] = v;
    return;
  }
  if (!rev[d]) {
    int M = L + R >> 1;
    if (x <= M) {
      upd(d - 1, 2 * idx, L, M, x, v);
    } else {
      upd(d - 1, 2 * idx + 1, M + 1, R, x, v);
    }
  } else {
    int M = L + R >> 1;
    if (x <= L + R - M - 1) {
      upd(d - 1, 2 * idx + 1, M + 1, R, x + M + 1 - L, v);
    } else {
      upd(d - 1, 2 * idx, L, M, x - R + M, v);
    }
  }
  seg[idx] = seg[2 * idx] + seg[2 * idx + 1];
}
inline long long qry(int d, int idx, int L, int R, int l, int r) {
  l = max(l, L);
  r = min(r, R);
  if (l <= r) {
    if (L == l && R == r) {
      return seg[idx];
    }
    if (!rev[d]) {
      int M = L + R >> 1;
      return qry(d - 1, 2 * idx, L, M, l, min(M, r)) +
             qry(d - 1, 2 * idx + 1, M + 1, R, max(M + 1, l), r);
    } else {
      int M = L + R >> 1;
      return qry(d - 1, 2 * idx + 1, M + 1, R, l + M + 1 - L, r + M + 1 - L) +
             qry(d - 1, 2 * idx, L, M, l - R + M, r - R + M);
    }
  }
  return 0;
}
inline void justPrint() {
  cout << "Array:\n";
  for (int i = 0; i < n; i++) {
    cout << qry(ln, 1, 0, n - 1, i, i) << " ";
  }
  cout << "\n";
}
int main() {
  ios ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> q;
  ln = n;
  n = 1 << n;
  for (int i = 0; i < n; i++) cin >> ar[i];
  bld(1, 0, n - 1);
  for (int i = 0; i < q; i++) {
    int t;
    cin >> t;
    if (t == 1) {
      int x, k;
      cin >> x >> k;
      upd(ln, 1, 0, n - 1, x - 1, k);
    } else if (t == 2) {
      int x;
      cin >> x;
      for (int i = x; i > 0; i--) {
        rev[i] ^= 1;
      }
    } else if (t == 3) {
      int x;
      cin >> x;
      rev[x + 1] ^= 1;
    } else {
      int l, r;
      cin >> l >> r;
      cout << qry(ln, 1, 0, n - 1, l - 1, r - 1) << "\n";
    }
  }
}
