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:   $Replace(x, k)$ — change $a_x$ to $k$;  $Reverse(k)$ — reverse each subarray $[(i-1) \cdot 2^k+1, i \cdot 2^k]$ for all $i$ ($i \ge 1$);  $Swap(k)$ — swap subarrays $[(2i-2) \cdot 2^k+1, (2i-1) \cdot 2^k]$ and $[(2i-1) \cdot 2^k+1, 2i \cdot 2^k]$ for all $i$ ($i \ge 1$);  $Sum(l, r)$ — 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 $n$, $q$ ($0 \le n \le 18$; $1 \le q \le 10^5$) — the length of array $a$ and the number of queries.

The second line contains $2^n$ integers $a_1, a_2, \ldots, a_{2^n}$ ($0 \le a_i \le 10^9$).

Next $q$ lines contains queries — one per line. Each query has one of $4$ types:   "$1$ $x$ $k$" ($1 \le x \le 2^n$; $0 \le k \le 10^9$) — $Replace(x, k)$;  "$2$ $k$" ($0 \le k \le n$) — $Reverse(k)$;  "$3$ $k$" ($0 \le k < n$) — $Swap(k)$;  "$4$ $l$ $r$" ($1 \le l \le r \le 2^n$) — $Sum(l, r)$. 

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:   $Sum(3, 7)$ $\to$ $8 + 8 + 7 + 1 + 5 = 29$;  $Reverse(1)$ $\to$ $\{0,7,8,8,1,7,2,5\}$;  $Swap(2)$ $\to$ $\{1,7,2,5,0,7,8,8\}$;  $Sum(1, 6)$ $\to$ $1 + 7 + 2 + 5 + 0 + 7 = 22$;  $Reverse(3)$ $\to$ $\{8,8,7,0,5,2,7,1\}$;  $Replace(5, 16)$ $\to$ $\{8,8,7,0,16,2,7,1\}$;  $Sum(8, 8)$ $\to$ $1$;  $Swap(0)$ $\to$ $\{8,8,0,7,2,16,1,7\}$.

Difficulty: interview

Starter code:

Solutions:
class BIT():
    def __init__(self,n):
        self.BIT=[0]*(n+1)
        self.num=n

    def query(self,idx):
        res_sum = 0
        while idx > 0:
            res_sum += self.BIT[idx]
            idx -= idx&(-idx)
        return res_sum

    #Ai += x O(logN)
    def update(self,idx,x):
        while idx <= self.num:
            self.BIT[idx] += x
            idx += idx&(-idx)
        return

n,q=map(int,input().split())
a=list(map(int,input().split()))
bit=BIT(2**n)
for i in range(2**n):
    bit.update(i+1,a[i])
b=0

def Sum(r,xor):
    id=xor
    res=0
    if r==-1:
        return res
    for i in range(n,-1,-1):
        if r>>i &1:
            L=(id>>i)<<i
            R=L+(1<<i)-1
            res+=bit.query(R+1)-bit.query(L)
            id^=(1<<i)
    return res


for _ in range(q):
    query=tuple(map(int,input().split()))
    if query[0]==1:
        g,x,k=query
        x-=1
        x^=b
        bit.update(x+1,k-a[x])
        a[x]=k
    elif query[0]==2:
        k=query[1]
        b^=2**k-1
    elif query[0]==3:
        k=query[1]
        if k!=n:
            b^=2**k
    else:
        gl,l,r=query
        l-=1
        test=Sum(r,b)-Sum(l,b)
        print(test)