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 long long MXN = 5e5 + 10;
const long long MXS = MXN * 4;
long long n, q;
long long A[MXN];
long long Seg[MXS], Lazy[MXS], LC[MXS], RC[MXS], Is_Rev[MXS];
void Build(long long id = 1, long long s = 1, long long e = n) {
  if (s == e) {
    Seg[id] = A[s];
    return;
  }
  LC[id] = (id * 2), RC[id] = (id * 2 + 1);
  Build((id * 2), s, ((s + e) / 2)), Build((id * 2 + 1), ((s + e) / 2 + 1), e);
  Seg[id] = Seg[(id * 2)] + Seg[(id * 2 + 1)];
}
inline void Shift(long long id, long long s, long long e) {
  Seg[id] += Lazy[id];
  if (s == e) {
    Lazy[id] = 0;
    return;
  }
  Lazy[(id * 2)] += Lazy[id], Lazy[(id * 2 + 1)] += Lazy[id];
  Lazy[id] = 0;
}
void Upd(long long ind, long long x, long long id = 1, long long s = 1,
         long long e = n) {
  Shift(id, s, e);
  if (e < ind || s > ind) return;
  if (s == e) {
    Seg[id] = x;
    return;
  }
  if (Is_Rev[(e - s + 1)]) swap(LC[id], RC[id]);
  Upd(ind, x, LC[id], s, ((s + e) / 2)),
      Upd(ind, x, RC[id], ((s + e) / 2 + 1), e);
  if (Is_Rev[(e - s + 1)]) swap(LC[id], RC[id]);
  Seg[id] = Seg[(id * 2)] + Seg[(id * 2 + 1)];
}
long long Get(long long l, long long r, long long id = 1, long long s = 1,
              long long e = n) {
  Shift(id, s, e);
  if (e < l || s > r) return 0;
  if (l <= s && e <= r) return Seg[id];
  if (Is_Rev[(e - s + 1)]) swap(LC[id], RC[id]);
  long long ans = Get(l, r, LC[id], s, ((s + e) / 2)) +
                  Get(l, r, RC[id], ((s + e) / 2 + 1), e);
  if (Is_Rev[(e - s + 1)]) swap(LC[id], RC[id]);
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> q, n = (1LL << n);
  for (int i = 1; i <= n; i++) cin >> A[i];
  Build();
  while (q--) {
    long long typ, x, k, l, r;
    cin >> typ;
    switch (typ) {
      case 1:
        cin >> x >> k;
        Upd(x, k);
        break;
      case 2:
        cin >> k;
        for (int i = 0; i <= k; i++) Is_Rev[(1LL << i)] = !Is_Rev[(1LL << i)];
        break;
      case 3:
        cin >> k;
        k++;
        Is_Rev[(1LL << k)] = !Is_Rev[(1LL << k)];
        break;
      case 4:
        cin >> l >> r;
        cout << Get(l, r) << '\n';
        break;
    }
  }
  return 0;
}
