Problem Description

A city in Canada where JOI lives is divided into a grid by $w$ roads running north-south and $h$ roads running east-west.

The $w$ north-south roads are numbered from west to east as $1, 2, \ldots, w$. The $h$ east-west roads are numbered from south to north as $1, 2, \ldots, h$. The intersection of the $i$-th north-south road and the $j$-th east-west road is represented as ($i, j$).

JOI lives near the intersection ($1, 1$) and commutes by car to the company near the intersection ($w, h$). The car can only move along the roads. To shorten the commuting time, JOI only moves east or north. Additionally, to reduce traffic accidents, the city has the following traffic rule:

• A car that turns at an intersection cannot turn again at the next intersection.

That is, turning at an intersection and then turning again after moving one block is not allowed. How many possible commuting routes are there for JOI?

Given $w$ and $h$, create a program that outputs the number of JOI's commuting routes modulo $100,000$.

Input Format

The input consists of one line with two integers $w, h$ ($2 \leq w \leq 100$, $2 \leq h \leq 100$) separated by a space. $w$ represents the number of north-south roads, and $h$ represents the number of east-west roads.

Output Format

The output consists of one line containing the number of JOI's commuting routes modulo $100,000$.

Sample Input and Output

Sample Input #1

3 4

Sample Output #1

5

Sample Input #2

15 15

Sample Output #2

43688

Notes/Hints

Sample Explanation 1

In the first input example, there are 5 possible commuting routes for JOI, as shown in the figure. Therefore, output 5.

Sample Explanation 2

In the second input example, there are 143,688 possible commuting routes for JOI. Therefore, output 43,688, which is 143,688 modulo 100,000.

见题面 Input 部分

见题面 Output 部分