G - The Debut Album URAL - 2018(dp)

Pop-group “Pink elephant” entered on recording their debut album. In fact they have only two songs: “My love” and “I miss you”, but each of them has a large number of remixes.

The producer of the group said that the album should consist of
n remixes. On second thoughts the musicians decided that the album will be of interest only if there are no more than
a remixes on “My love” in a row and no more than b remixes on “I miss you” in a row. Otherwise, there is a risk that even the most devoted fans won’t listen to the disk up to the end.

How many different variants to record the album of interest from
n remixes exist? A variant is a sequence of integers 1 and 2, where ones denote remixes on “My love” and twos denote remixes on “I miss you”. Two variants are considered different if for some
i in one variant at i-th place stands one and in another variant at the same place stands two.

Input

The only line contains integers n, a,
b (1 ≤ a, b ≤ 300; max( a, b) + 1 ≤
n ≤ 50 000).

Output

Output the number of different record variants modulo 10
9+7.

Example

input	output
3 2 1	4

Notes

In the example there are the following record variants: 112, 121, 211, 212.

#include <iostream>
#include<cstring>
#include<cstdio>
using namespace std;

const int maxn=50000+5;
const int INF=1e9+7;
int dp[maxn][5];
int main()
{
int n,a,b;
while(cin>>n>>a>>b)
{

memset(dp,0,sizeof(dp));
dp[0][1]=1;
dp[0][2]=1;
for(int i=0;i<=n;i++)
{
for(int j=1; j+i<=n && j<=b; j++)
{
dp[i+j][1] += dp[i][2];
dp[i+j][1]%=INF;
}
for(int j=1; j+i <= n && j <= a; j++)
{
dp[i+j][2]+=dp[i][1];
dp[i+j][2]%=INF;
}
}
cout<<((dp
[1]+dp
[2])%INF)<<endl;

}
return 0;
}