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 N = 1e6 + 10;
const long long mod = 1e9 + 7;
inline long long read() {
  long long X = 0;
  bool flag = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') flag = 0;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    X = (X << 1) + (X << 3) + ch - '0';
    ch = getchar();
  }
  if (flag) return X;
  return ~(X - 1);
}
long long n, m, k, x, y;
long long ans;
int ar[N];
int re[N];
struct segt {
  long long sm;
} c[N];
void pushup(int x) { c[x].sm = c[x << 1].sm + c[x << 1 | 1].sm; }
void build(int l, int r, int x) {
  if (l == r) {
    c[x].sm = read();
    return;
  }
  int md = l + r >> 1;
  build(l, md, x << 1);
  build(md + 1, r, x << 1 | 1);
  pushup(x);
}
void update(int pos, int v, int x, int dep, int L, int R) {
  if (pos < L || pos > R) return;
  if (L == R && L == pos) {
    c[x].sm = v;
    return;
  }
  int md = L + R >> 1;
  update(pos, v, x << 1 | re[dep], dep - 1, L, md);
  update(pos, v, x << 1 | re[dep] ^ 1, dep - 1, md + 1, R);
  pushup(x);
}
long long gtsm(int l, int r, int x, int dep, int L, int R) {
  if (L >= l && R <= r) return c[x].sm;
  int md = L + R >> 1;
  long long res = 0;
  if (l <= md) res += gtsm(l, r, x << 1 | re[dep], dep - 1, L, md);
  if (r > md) res += gtsm(l, r, x << 1 | re[dep] ^ 1, dep - 1, md + 1, R);
  return res;
}
void swp(int k) { re[k + 1] ^= 1; }
void reve(int k) {
  for (register int i(0); i <= k; ++i) re[i] ^= 1;
}
void solvve() {
  n = read();
  int q = read();
  build(1, 1 << n, 1);
  while (q--) {
    int op, x, y;
    op = read();
    x = read();
    if (op == 1) {
      y = read();
      update(x, y, 1, n, 1, 1 << n);
    } else if (op == 2) {
      reve(x);
    } else if (op == 3) {
      swp(x);
    } else {
      y = read();
      cout << gtsm(x, y, 1, n, 1, 1 << n) << endl;
    }
  }
}
int main() {
  { solvve(); }
  return 0;
}
