Light OJ: 1095 – Arrange the Numbers

Problem Link : http://lightoj.com:81/volume/problem/1095


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

ll fact[1005];

ll dp[1005][1005];

ll nCk(int n, int k)
{
    if(k==1) return n;
    if(n==k) return 1;

    if(dp[n][k]!=-1) return dp[n][k];

    return dp[n][k]= (nCk(n-1,k-1)+nCk(n-1,k))%MOD;
}


int main()
{

    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);

    fact[0]=1;

    for(ll i=1; i<1002; i++) fact[i]=(fact[i-1]*i)%MOD;

    int t;
    sf(t);
    ms(dp,-1);

    TEST_CASE(t)
    {
        ll n,m,k;
        sfffl(n,m,k);
        ll ans=nCk(m,k);

        int nn=n-k;

        ll ans1=fact[n-k];

        for(int i=1; i<=(m-k); i++)
        {
            if(i%2==1)
                ans1-= (nCk(m-k,i)*fact[nn-i])%MOD;
            else
                ans1+= (nCk(m-k,i)*fact[nn-i])%MOD;
            ans1=(ans1+MOD)%MOD;
        }

        PRINT_CASE;

        printf("%lld\n",(ans*ans1)%MOD);


    }


    return 0;
}

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