Codeforces Round #273 (Div. 2) D. Red-Green Towers

D. Red-Green Towers

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

There are r red and g green blocks for construction of the red-green tower. Red-green tower can be built following next rules:

• Red-green tower is consisting of some number of levels;

• Let the red-green tower consist of n levels, then the first level of this tower should consist of n blocks, second level — of n - 1 blocks, the third one — of n - 2 blocks, and so on — the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one;

• Each level of the red-green tower should contain blocks of the same color.

Let h be the maximum possible number of levels of red-green tower, that can be built out of r red and g green blocks meeting the rules above. The task is to determine how many different red-green towers having h levels can be built out of the available blocks.

Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.

You are to write a program that will find the number of different red-green towers of height h modulo 10⁹ + 7.

Input

The only line of input contains two integers r and g, separated by a single space — the number of available red and green blocks respectively (0 ≤ r, g ≤ 2·10⁵, r + g ≥ 1).

Output

Output the only integer — the number of different possible red-green towers of height h modulo 10⁹ + 7.

Sample test(s)

Input

4 6

Output

2

Input

9 7

Output

6

Input

1 1

Output

2

  给你红色和绿色方块的个数，一层只能放一种颜色，问在堆最高层的情况下有多少种堆法。

  首先根据方块总数算出最高层数h。dp[i][j]表示堆到第i层用j个红方块的堆放种数，但是二维开不下，用滚动数组。最后答案就是dp[h][i]的和，i是堆到最高层红方块的个数范围。

#include<iostream>
#include<queue>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<set>
#include<map>
#include<vector>
#include<stack>
#include<algorithm>
#define eps 1e-9
#define INF 0x3f3f3f3f
#define MAXN 200010
#define MAXM 55
#define MAXNODE 100010*4
#define MOD 1000000007
typedef long long LL;
using namespace std;
int R,G;
LL dp[MAXN];
int main(){
    //freopen("in.txt","r",stdin);
    while(scanf("%d%d",&R,&G)!=EOF){
        memset(dp,0,sizeof(dp));
        dp[0]=1;
        LL h=0,cnt=0;
        for(int i=1;;i++){
            cnt+=i;
            if(cnt>R+G) break;
            h=i;
        }
        for(int i=1;i<=h;i++)
            for(int j=R;j>=i;j--) dp[j]=(dp[j]+dp[j-i])%MOD;
        LL sum=h*(h+1)/2,ans=0;
        if(sum-G<0) sum=0;
        else sum-=G;
        for(int i=sum;i<=R;i++) ans=(ans+dp[i])%MOD;
        printf("%I64d\n",ans);
    }
    return 0;
}