Codeforces Round 738 (Div. 2) |
---|
Finished |
Mocha wants to be an astrologer. There are $$$n$$$ stars which can be seen in Zhijiang, and the brightness of the $$$i$$$-th star is $$$a_i$$$.
Mocha considers that these $$$n$$$ stars form a constellation, and she uses $$$(a_1,a_2,\ldots,a_n)$$$ to show its state. A state is called mathematical if all of the following three conditions are satisfied:
Here, $$$\gcd(a_1,a_2,\ldots,a_n)$$$ denotes the greatest common divisor (GCD) of integers $$$a_1,a_2,\ldots,a_n$$$.
Mocha is wondering how many different mathematical states of this constellation exist. Because the answer may be large, you must find it modulo $$$998\,244\,353$$$.
Two states $$$(a_1,a_2,\ldots,a_n)$$$ and $$$(b_1,b_2,\ldots,b_n)$$$ are considered different if there exists $$$i$$$ ($$$1\le i\le n$$$) such that $$$a_i \ne b_i$$$.
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 50$$$, $$$1 \le m \le 10^5$$$) — the number of stars and the upper bound of the sum of the brightness of stars.
Each of the next $$$n$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \le l_i \le r_i \le m$$$) — the range of the brightness of the $$$i$$$-th star.
Print a single integer — the number of different mathematical states of this constellation, modulo $$$998\,244\,353$$$.
2 4 1 3 1 2
4
5 10 1 10 1 10 1 10 1 10 1 10
251
5 100 1 94 1 96 1 91 4 96 6 97
47464146
In the first example, there are $$$4$$$ different mathematical states of this constellation:
Name |
---|