【CodeForces - 1105C】Ayoub and Lost Array（线性计数dp）

题干：

Ayoub had an array aa of integers of size nn and this array had two interesting properties:

All the integers in the array were between ll and rr (inclusive).
The sum of all the elements was divisible by 33.

Unfortunately, Ayoub has lost his array, but he remembers the size of the array nnand the numbers ll and rr, so he asked you to find the number of ways to restore the array.

Since the answer could be very large, print it modulo 109+7109+7 (i.e. the remainder when dividing by 109+7109+7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 00.

Input

The first and only line contains three integers nn, ll and rr (1≤n≤2⋅105,1≤l≤r≤1091≤n≤2⋅105,1≤l≤r≤109) — the size of the lost array and the range of numbers in the array.

Output

Print the remainder when dividing by 109+7109+7 the number of ways to restore the array.

Examples

Input

2 1 3

Output

Input

3 2 2

Output

Input

9 9 99

Output

711426616

Note

In the first example, the possible arrays are : [1,2],[2,1],[3,3][1,2],[2,1],[3,3].

In the second example, the only possible array is [2,2,2][2,2,2].

解题报告：

dp[i][j]表示选择i个数可以组成模数为j的方案数。

AC代码：

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<queue>
#include<map>
#include<vector>
#include<set>
#include<string>
#include<cmath>
#include<cstring>
#define ll long long
#define pb push_back
#define pm make_pair
using namespace std;
const int MAX = 2e5 + 5;
const ll mod = 1e9+7;
int n,l,r;
ll dp[MAX][3],num[3];
int main()
{cin>>n>>l>>r;ll tmp = (r-l)/3;num[0] = r/3 - (l-1)/3;num[1] = (r+2)/3 - (l+1)/3;num[2] = (r+1)/3 - (l)/3;dp[0][0]=1;for(int i = 1; i<=n; i++) {for(int j = 0; j<3; j++) {for(int k = 0; k<3; k++) {dp[i][j] += dp[i-1][k]*num[(j+3-k)%3];}dp[i][j]%=mod;}}    printf("%lld\n",dp[n][0]);return 0 ;
}

也可以直接dp[1][0,1,2]都给初始化好。

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【CodeForces - 1105C】Ayoub and Lost Array（线性计数dp）

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