I. Stairway To Heaven
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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:

  1. 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.
  2. 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 $$$a \lt b$$$ and the number of common divisors between $$$a$$$ and $$$b$$$ is $$$1$$$.
  3. 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.
Bob realized that the game was too easy for him. To make the game exciting, Alice asked him the number of different paths he can take to reach heaven from hell. As the answer might be big, print the number of paths modulo $$$998244353$$$.
Input

The only line contains two positive integers $$$u$$$ and $$$v$$$ ($$$ 2 \le u \lt v\le 10^5$$$) 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 $$$998244353$$$.

Examples
Input
2 5
Output
3
Input
69 69420
Output
81268163
Note

For the sample test, the following $$$3$$$ paths are valid:

  1. $$$2 \rightarrow 3 \rightarrow 4 \rightarrow 5$$$
  2. $$$2 \rightarrow 3 \rightarrow 5$$$
  3. $$$2 \rightarrow 5$$$
He can't directly go to $$$4$$$ from $$$2$$$ because there are more than $$$1$$$ common divisors between them ($$$1,2$$$). Also, note that he cannot go from $$$3$$$ to $$$2$$$ because he can't go to a smaller number.