Problem Statement

You are given positive integers N and M. Here, it is guaranteed that $N\leq M \leq 2N$.
Print the sum, modulo 200\ 003 (a prime), of the following value over all sequences of positive integers $S=(S_1,S_2,\dots,S_N)$ such that $\displaystyle \sum_{i=1}^{N} S_i = M$ (notice the unusual modulo):

• $\displaystyle \prod_{k=1}^{N} \min(k,S_k)$.

Input

The input is given from Standard Input in the following format:
N M

Output

Print the answer as an integer.

Constraints

• $1 \leq N \leq 10^{12}$
• $N \leq M \leq 2N$
• All values in the input are integers.

Sample Input 1

3 5

Sample Output 1

14

There are six sequences S that satisfy the condition:
S=(1,1,3), S=(1,2,2), S=(1,3,1), S=(2,1,2), S=(2,2,1), S=(3,1,1).
The value $\displaystyle \prod_{k=1}^{N} \min(k,S_k)$ for each of those S is as follows.

• S=(1,1,3) : $1\times 1 \times 3 = 3$
• S=(1,2,2) : $1\times 2 \times 2 = 4$
• S=(1,3,1) : $1\times 2 \times 1 = 2$
• S=(2,1,2) : $1\times 1 \times 2 = 2$
• S=(2,2,1) : $1\times 2 \times 1 = 2$
• S=(3,1,1) : $1\times 1 \times 1 = 1$

Thus, you should print their sum: 14.

Sample Input 2

1126 2022

Sample Output 2

40166

Print the sum modulo 200\ 003.

Sample Input 3

1000000000000 1500000000000

Sample Output 3

180030

见题面 Input 部分

见题面 Output 部分