[递推+矩阵快速幂]Codeforces 1117D - Magic Gems

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
#define _____ ios::sync_with_stdio(false);cin.tie(0);
const int M = 1e9 + 7;
//head

ll n,m;
struct Mat{
    ll a[102][102];
};
Mat mul(const Mat & a,const Mat & b){
    Mat ans;
    for(int i = 1; i <= m; i++){
        for(int j = 1; j <= m; j++){
            ans.a[i][j] = 0;
            for(int k = 1; k <= m; k++){
                ans.a[i][j] += a.a[i][k]*b.a[k][j];
                if(ans.a[i][j] > M)ans.a[i][j] %= M;
            }
        }
    }
    return ans;
}
Mat quick_pow(Mat a,ll b){
    Mat t;
    for(int i = 1; i <= m; i++)t.a[i][i] = 1;
    while(b){
        if(b & 1)t = mul(t,a);
        b >>= 1;
        a = mul(a,a);
    }
    return t;
}
int main(){
    //freopen("data.in","r",stdin);
    _____
    cin >> n >> m;
    if(n < m){cout << 1 << ‘\n‘;}
    else{
        Mat ans,t;
        for(int i = 1; i < m; i++){
            ans.a[i+1][i] = 1;
        }
        ans.a[1][m] = ans.a[m][m] = 1;
        ans = quick_pow(ans,n-m);
        Mat a;
        for(int i = 1; i < m; i++)a.a[1][i] = 1;
        a.a[1][m] = 2;
        a = mul(a,ans);
        cout << a.a[1][m] << ‘\n‘;
    }
    return 0;
}