# URAL 2018. The Debut Album （dp）

## Description

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 109+7.

## Sample input

3 2 1


## Sample output

4


## 思路

dp[i][k] 代表长度为 i 的数列，以 k 结尾并满足题意的个数。

## AC 代码

#include<bits/stdc++.h>
using namespace std;

const int mod=1e9+7;

int dp[51000][2];

int main()
{
int n,a,b;
cin>>n>>a>>b;
dp[0][0]=dp[0][1]=1;
for(int i=1; i<=n; i++)
{
for(int j=1; j<=min(i,a); j++)
dp[i][0]=(dp[i][0]+dp[i-j][1])%mod;
for(int j=1; j<=min(i,b); j++)
dp[i][1]=(dp[i][1]+dp[i-j][0])%mod;
}
cout<<(dp[n][0]+dp[n][1])%mod;
return 0;
}