Problem Description

It is said that the great poet Li Bai loved drinking all his life. Luckily, he never drove.

One day, he carried a wine pot and left home. There were $2$ dou of wine in the pot. As he walked, he sang:

Walking on the street with nothing to do, carrying the pot to buy wine.
When he meets a shop, the amount doubles; when he meets flowers, he drinks one dou.

Along the way, he met shops $N$ times and met flowers $M$ times. It is known that the last thing he met was flowers, and he drank the wine exactly to $0$.

Please compute how many different possible orders of meeting shops and flowers there are on this trip.

Note: It is allowed to meet a shop when there is no wine in the pot ($0$ dou). After doubling, it is still $0$. However, it is not allowed to meet flowers when there is no wine.

Input Format

The first line contains two integers $N$ and $M$.

Output Format

Output one integer representing the answer. Since the answer may be very large, output it modulo $1000000007$ (i.e. $10^9+7$).

5 10

14

Hint

Sample Explanation

If we use 0 to represent meeting flowers and 1 to represent meeting a shop, the $14$ possible orders are as follows:

010101101000000
010110010010000
011000110010000
100010110010000
011001000110000
100011000110000
100100010110000
010110100000100
011001001000100
100011001000100
100100011000100
011010000010100
100100100010100
101000001010100

Constraints and Notes

For $40\%$ of the testdata: $1 \leq N, M \leq 10$.

For $100\%$ of the testdata: $1 \leq N, M \leq 100$.

Lanqiao Cup 2022 Provincial Contest B Group, Problem I.

Translated by ChatGPT 5