Problem Link : http://www.spoj.com/problems/AMR10E/
#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));} /*------------------------------------------------*/ /*----------------------Matrix-----------------------*/ // int MOD= ll MOD= 1000000007; struct matrix { ll mat[11][11]; int row,col; matrix() { row=col=0; memset(mat,0,sizeof mat); } matrix(int a, int b) { row=a,col=b; memset(mat,0,sizeof mat); } matrix operator*(const matrix &p) const { assert(col == p.row); matrix temp; temp.row = row; temp.col = p.col; for (int i = 0; i < temp.row; i++) { for (int j = 0; j < temp.col; j++) { ll sum = 0; for (int k = 0; k <col; k++) { sum += ((mat[i][k]%MOD) * (p.mat[k][j]%MOD))%MOD; sum%=MOD; } temp.mat[i][j] = sum; } } return temp; } matrix operator+ (const matrix &p) const { assert(row==p.row && col==p.col); matrix temp; temp.row=row; temp.col=col; for(int i=0; i<temp.row; i++) { for(int j=0; j<temp.col; j++) temp.mat[i][j]=((mat[i][j]%MOD)+(p.mat[i][j]%MOD))%MOD;; } return temp; } matrix identity() { matrix temp; temp.row=row; temp.col=col; for(int i=0; i<row; i++) temp.mat[i][i]=1; return temp; } matrix pow(ll pow) { matrix temp=(*this); matrix ret=(*this).identity(); while(pow) { if(pow % 2==1) ret=ret*temp; temp=temp*temp; pow/=2; } return ret; } void show() { printf("-----------------------------\n"); for(int i=0; i<row; i++) { for(int j=0; j<col; j++) printf("%lld ",mat[i][j]); printf("\n"); } printf("-----------------------------\n"); } }; /*--------------------------Matrix End---------------------*/ matrix identity; matrix func(matrix m, ll p) { // if(p==0) return identity; if(p==1) return identity; // // matrix ret=func(m,p/2); // // matrix temp=m.pow(p/2); if(p%2==0) { return func(m,p/2)*(identity+m.pow(p/2)); } else { return func(m,p-1)+m.pow(p-1); } } ll s[15],ara[15]; int main() { // freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); int t; sf(t); TEST_CASE(t) { ll n,r,k; sfffl(n,r,k); matrix base(r,1); ms(s,0); ms(ara,0); for(int i=1; i<=r; i++) sfl(s[i]); matrix a(r,r); for(int i=0; i<r; i++) { sfl(a.mat[0][i]); ara[i+1]=a.mat[0][i]; if(i+1!=r) a.mat[i+1][i]=1; } // base.show(); // a.show(); a=a.pow(k); // a.show(); // base.show(); identity=a.identity(); a=func(a,n); // a.show(); ll ans=0; if(k>r) { for(int i=r+1; i<=k; i++) { for(int j=1; j<=r; j++) { s[i]+=s[i-j]*ara[j]; s[i]%=MOD; } } for(int i=0; i<r; i++) { ans=(ans+(s[k-i]*a.mat[0][i])%MOD); ans%=MOD; } } else { for(int i=0; i<r; i++) { ans=(ans+(a.mat[r-k][r-i-1]*s[i+1])%MOD); ans%=MOD; } } pf("%lld\n",ans); } return 0; }