Problem Description

Relevant sentences to the problem have been bolded.

  “First, there is a magical number $a$.”
  “Tian Yi is very hungry, so let's give her $2^{a+2}$ egg tarts.”
  “I want more!”
  “Then... there is another magical number $b$, Tian Yi can get $b$ times the egg tarts!”
  “Wow! Then I have $k=b \times 2^{a+2}$ egg tarts!”
  “Tian Yi likes round numbers, so let's round it up, give her $p=\lceil \frac{k}{25}\rceil \times 100$ egg tarts!”
  “A Ling is so nice!”
  “Here you go\~.” A Ling笑着抚过天依的脑袋，从袋子里拿出寥寥几个蛋挞。
  “Huh?!”
  “Finally, Tian Yi can't eat too much, so $p$ should be taken modulo $\color{black} 998 \color{red}3 \color{black} 44353$.”
  “…Indeed, a bad egg.”

Now Tian Yi wants to know, for the given $a$ and $b$ from A Ling, how many egg tarts she can actually get, i.e., the result of $p \bmod \color{black} 998 \color{red}3 \color{black} 44353$.

Note: $\lceil x \rceil$ refers to rounding $x$ up.

Input Format

A single line containing two integers, representing $b$ and $a$ respectively.

Please note the order of input.

Output Format

A single line containing an integer $p$, representing the number of egg tarts Tian Yi can get.

Sample Input and Output

Sample Input #1

30 1

Sample Output #1

1000

Sample Input #2

60 15

Sample Output #2

31457300

Sample Input #3

2020 412

Sample Output #3

133047246

Notes/Hints

Sample Explanation #2

$k=60 \times 2^{(15+2)}=7864320$, $p=\lceil \frac{k}{25} \rceil \times 100 =31457300$.

Data Range

This problem uses batched testing.

• Subtask 1 (20 Points): $a, b \leq 100$ and $b \equiv 0 \pmod{25}$.
• Subtask 2 (50 Points): $b \leq 10^9$.
• Subtask 3 (30 Points): No special constraints on the data.

For $100\%$ of the data, $20 \leq b \leq 10^{10010}$, $1 \leq a \leq 10^{18}+8$.

见题面 Input 部分

见题面 Output 部分