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Segment

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 336    Accepted Submission(s): 55


Problem Description
ZY found a weird segment tree with range [1, n].
For one node [a, b] (a<b) we choose a random integer x in range [a, b), seperate the segment into [a,x] and [x+1,b].
While doing query on this segment tree, bad thing happens. For one query [l, r]. If we want to obtain the information of the range [l, r], what is the expected number of nodes in the segment tree that would be visited?
For example, when querying range [2,4] in this segment tree, we will visit nodes in red.
 

Input
The first line contains two integer n,q.
The following q lines each contain a query interval [l,r].
$1 \leq n,q \leq 10^6$.
 

Output
For each query, output the expected number of visited nodes in a line, modulo 998244353.
 

Sample Input
2 3 1 1 2 2 1 2
 

Sample Output
2 2 1
 

Source
 

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