Stairway To Heaven
Description
Alice and Bob found a divine stairway when they went on an adventure to the seventh sky. As always, they decided to play a game with it. The rules of the game are following:
- The first step is labeled by a positive integer $u$, and the labels of the following steps are increased by $1$ sequentially all the way up to $v$ which is the topmost step of the stairway.
- Bob can not simply walk up the stairs due to its divine characteristics. But with the power of his infinity stones, he can teleport from step $a$ to step $b$ if and only if $a < b$ and the number of common divisors between $a$ and $b$ is $1$.
- Bob is currently at step $u$ which they are calling hell and he must reach step $v$ which they are calling heaven to win the game.
The only line contains two positive integers $u$ and $v$ ($ 2 \le u < v\le 10^5$) denoting the label of hell and heaven respectively.
Print the number of different ways Bob can reach heaven from hell in a single line. The answer might be very big. So print the answer modulo $998244353$.
Input
The only line contains two positive integers $u$ and $v$ ($ 2 \le u < v\le 10^5$) denoting the label of hell and heaven respectively.
Output
Print the number of different ways Bob can reach heaven from hell in a single line. The answer might be very big. So print the answer modulo $998244353$.
2 5
69 69420
3
81268163
Note
For the sample test, the following $3$ paths are valid:
- $2 \rightarrow 3 \rightarrow 4 \rightarrow 5$
- $2 \rightarrow 3 \rightarrow 5$
- $2 \rightarrow 5$