You are given following:- - an array A consisting of N positive integers - Q queries of the form L,R,M

consider all subsequences of subarray from L to R of size M.

Determine the sum of Bitwise OR of all these subsequences. Bitwise OR of an empty subsequence is 0. If there is no Subsequence of Length M, print 0.

- print the output with mod 998244353.
- A subsequence is a sequence that can be derived from the given sequence by deleting 0 or more elements without changing the order of the remaining elements.
- 1 based indexing is followed.

Example A=[1,2,3] Q=[1,3,2] // L,R,M

subarray= [1,2,3] for this we have 3 subsequences of length 2. - [1,2] [2,3] [1,3]

Bitwise OR of all above subsequences is 3+3+3=9 , so output is 9

constraints as below

I have tried solving above using Bit-manipulation but it works only for small test cases. i can post my solution as well if you want

Operate on each bit separately. For ith bit = ((r-l+1,m)-(# off bits,m))*2^i , where (a,b) is binomial coefficient.

Hi could you elaborate little more? i m kind of beginner, so could not connect much. may be small example would be useful. thanks

This should help if you aren't the same guy who posted it there too.

I am not the same. But Thanks

Let's rephrase this problem , consider a binary sequence [0,0,0,1,1,1] how many sub sequences exist of a given sequence having length m such that it contains at least single 1 ?? (# sub sequence of length m — # sub sequence containing only 0)

let consider each bit at a time.let p be the no of ones and q be the no of zeroes at ith bit.your answer will be summation of c(p,k)*c(q,m-k)*(1<<i-1) ,where k is from 1 to m.