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;
inline int read() {
  register int x = 0, c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while ('0' <= c && c <= '9') x = 10 * x + (c ^ 48), c = getchar();
  return x;
}
const int MAXL = (1 << 18) + 5;
struct node {
  node *lc, *rc;
  int rev, swp;
  bool turn;
  long long sum;
} tr[MAXL << 1];
node *ncnt = &tr[0];
node *root;
inline void Pushdown(node *rt, const int dep) {
  if (rt->rev & (1 << dep)) {
    rt->lc->rev ^= (1 << (dep - 1));
    rt->rc->rev ^= (1 << (dep - 1));
    rt->rev ^= (1 << dep);
    swap(rt->lc, rt->rc);
  }
  rt->lc->rev ^= rt->rev;
  rt->rc->rev ^= rt->rev;
  rt->rev = 0;
  if (rt->swp & (1 << dep)) {
    rt->swp ^= (1 << dep);
    swap(rt->lc, rt->rc);
  }
  rt->lc->swp ^= rt->swp;
  rt->rc->swp ^= rt->swp;
  rt->swp = 0;
}
inline void Pushup(node *rt) { rt->sum = rt->lc->sum + rt->rc->sum; }
inline void Build(node *&rt, const int dep) {
  if (!rt) rt = ncnt++;
  if (!dep) {
    rt->sum = read();
    return;
  }
  Build(rt->lc, dep - 1);
  Build(rt->rc, dep - 1);
  Pushup(rt);
}
inline void Replace(node *rt, const int dep, const int x, const int k) {
  if (!dep) {
    rt->sum = k;
    return;
  }
  Pushdown(rt, dep);
  if (x & (1 << (dep - 1)))
    Replace(rt->rc, dep - 1, x, k);
  else
    Replace(rt->lc, dep - 1, x, k);
  Pushup(rt);
}
inline long long Query(node *rt, const int dep, const int l, const int r,
                       const int L, const int R) {
  if (L <= l && r <= R) return rt->sum;
  Pushdown(rt, dep);
  int mid = (l + r) >> 1;
  if (R <= mid) return Query(rt->lc, dep - 1, l, mid, L, R);
  if (L > mid) return Query(rt->rc, dep - 1, mid + 1, r, L, R);
  return Query(rt->lc, dep - 1, l, mid, L, R) +
         Query(rt->rc, dep - 1, mid + 1, r, L, R);
}
int n, q, ml;
int main() {
  n = read(), q = read(), ml = 1 << n;
  Build(root, n);
  for (int i = 1, k; i <= q; i++) {
    switch (read()) {
      case 1:
        k = read(), Replace(root, n, k - 1, read());
        break;
      case 2:
        root->rev ^= (1 << read());
        break;
      case 3:
        root->swp ^= (1 << (read() + 1));
        break;
      case 4:
        k = read(), printf("%lld\n", Query(root, n, 1, ml, k, read()));
        break;
    }
  }
  return 0;
}
