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;
template <typename A>
void _do(A x) {
  cerr << x << "\n";
}
template <typename A, typename... B>
void _do(A x, B... y) {
  cerr << x << ", ";
  _do(y...);
}
long long N, n, q;
long long seg[1200005], arr[300005];
long long rev[20], swp[20];
void build(long long l, long long r, long long idx) {
  if (l == r) {
    seg[idx] = arr[l];
    return;
  }
  long long m = (l + r) / 2;
  build(l, m, idx * 2);
  build(m + 1, r, idx * 2 + 1);
  seg[idx] = seg[idx * 2] + seg[idx * 2 + 1];
}
void modify(long long l, long long r, long long idx, long long dep,
            long long re, long long pos, long long val) {
  if (l == r) {
    assert(dep == 0);
    seg[idx] = val;
    return;
  }
  long long m = (l + r) / 2;
  re ^= rev[dep];
  long long cp = re ^ swp[dep];
  if (cp) {
    if (pos <= m)
      pos += 1 << (dep - 1);
    else
      pos -= 1 << (dep - 1);
  }
  if (pos <= m)
    modify(l, m, idx * 2, dep - 1, re, pos, val);
  else
    modify(m + 1, r, idx * 2 + 1, dep - 1, re, pos, val);
  seg[idx] = seg[idx * 2] + seg[idx * 2 + 1];
}
long long query(long long l, long long r, long long idx, long long dep,
                long long re, long long ql, long long qr) {
  if (ql <= l && r <= qr) return seg[idx];
  long long m = (l + r) / 2;
  re ^= rev[dep];
  long long cp = re ^ swp[dep];
  if (cp) {
    if (qr <= m) {
      ql += 1 << (dep - 1);
      qr += 1 << (dep - 1);
      return query(m + 1, r, idx * 2 + 1, dep - 1, re, ql, qr);
    } else if (ql > m) {
      ql -= 1 << (dep - 1);
      qr -= 1 << (dep - 1);
      return query(l, m, idx * 2, dep - 1, re, ql, qr);
    } else {
      long long q1l = ql, q1r = m, q2l = m + 1, q2r = qr;
      q1l += 1 << (dep - 1);
      q1r += 1 << (dep - 1);
      q2l -= 1 << (dep - 1);
      q2r -= 1 << (dep - 1);
      return query(m + 1, r, idx * 2 + 1, dep - 1, re, q1l, q1r) +
             query(l, m, idx * 2, dep - 1, re, q2l, q2r);
    }
  } else {
    if (qr <= m) return query(l, m, idx * 2, dep - 1, re, ql, qr);
    if (ql > m) return query(m + 1, r, idx * 2 + 1, dep - 1, re, ql, qr);
    return query(l, m, idx * 2, dep - 1, re, ql, qr) +
           query(m + 1, r, idx * 2 + 1, dep - 1, re, ql, qr);
  }
}
signed main() {
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> n >> q;
  N = 1 << n;
  for (long long i = 1; i <= N; i++) cin >> arr[i];
  build(1, N, 1);
  for (long long i = 1, ope, a, b; i <= q; i++) {
    cin >> ope;
    if (ope == 1) {
      cin >> a >> b;
      arr[a] = b;
      modify(1, N, 1, n, 0, a, b);
    } else if (ope == 2) {
      cin >> a;
      rev[a] ^= 1;
    } else if (ope == 3) {
      cin >> a;
      swp[a + 1] ^= 1;
    } else {
      cin >> a >> b;
      cout << query(1, N, 1, n, 0, a, b) << '\n';
    }
  }
}
