Warm up 3 [H] Skill

你为何这么叼！

[H] Skill

 

Yasser is an Egyptian coach; he will be organizing a training camp in Jordan. At the end of camp, Yasser was quiet amazed that the participants solved all of the hard problems he had prepared; so he decided to give them one last challenge: 
Print the number of integers having N digits where the digits form a non decreasing sequence. 

Input Specification
Input will start with T <= 100 number of test cases. Each test case consists of a single line having integer N where 1 <= N <= 100000.

 
Output Specification
For each test case print on a separate line the number of valid sequences modulo 1000000007. 

Sample Input
3

2

3

4 

Sample Output
55

220

715

 

#include <cstdio>
#include <vector>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;
#define maxn 100005
#define mod 1000000007
#define ll long long
int n,m;
ll a[maxn];
int ex_gcd(int a,int b,int &x,int &y){
    int res;
    if(!b){x=1;y=0;return a;}
    res=ex_gcd(b,a%b,y,x);
    y-=x*(a/b);
    return res;
}
int main(){
    int t;
    a[1]=10;
    for(int i=2;i<maxn;i++){
        a[i]=a[i-1]*(9+i)%mod;
        int x,y;
        ex_gcd(i,mod,x,y);
        a[i]=a[i]*((x+mod)%mod)%mod;
    }
    scanf("%d",&t);
    while(t--){
        scanf("%d",&n);
        printf("%I64d\n",a[n]);
    }
    return 0;
}