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Bob And Array Queries

Advanced Data Structures, Data Structures, Segment Trees


Bob has an array A[] of N integers. Initially, all the elements of the array are zero. Bob asks you to perform Q operations on this array.

There are three types of operations that can be performed:

  1.  1 X: Update the value of A[X] to  2 * A[X] + 1.
  2.  2 X: Update the value A[X] to \(\lfloor\) A[x]/2 \(\rfloor\), where \(\lfloor\)\(\rfloor\) is Greatest Integer Function.
  3.  3 X Y: Take all the A[i] such that  X <= i <= Y and convert them into their corresponding binary strings. Now concatenate all the binary strings and find the total no. of '1' in the resulting string.

Note: It is guaranteed that there is at least 1 type-3 query in the every test case. All the array elements will fit into 64 bit integers.

Input Format:
First line consists of two space-separated integers N and Q.
Next, Q lines consist of Q operations of either of the 3 types as described above.

Output Format:
For each type-3 query print the answer that is the no. of '1' in the resulting string.

\(1 \le N,Q \le 500000\)
\(1 \le X \le Y \le N\)



5 5
1 1
1 2
1 3
3 1 3
3 2 4

Initially, A=[0,0,0,0,0]

After 1st query, A=[1,0,0,0,0]

After 2nd query, A=[1,1,0,0,0]

After 3rd query, A=[1,1,1,0,0]

For 4th query, no. of '1' in binary representation of A[1]=A[2]=A[3]=1. So, answer=3.

For 5th query, answer is 2.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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