Submission #68670906

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;

const int MOD = 1e9 + 7; //1000000007

/*
組み合わせ計算の方法およびソースコードは
https://algo-logic.info/combination/
を参照した
*/

vector<long long> fact_inv, inv;


/*  init_nCk :二項係数のための前処理
    計算量:O(k)
*/
void init_nCk(int SIZE) {
    fact_inv.resize(SIZE + 5);
    inv.resize(SIZE + 5);
    fact_inv[0] = fact_inv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < SIZE + 5; i++) {
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
        fact_inv[i] = fact_inv[i - 1] * inv[i] % MOD;
    }
}
/*  nCk :MODでの二項係数を求める(前処理 int_nCk が必要)
    計算量:O(k)
*/
long long nCk(int n, int k) {
    assert(!(n < k));
    assert(!(n < 0 || k < 0));
    long long ans = 1;
    for (int i = n; i >= n - k + 1; i--) {
        ans *= i;
        ans %= MOD;
    }
    return ans * fact_inv[k] % MOD;
}

int main(){
    int stairs_number, jump_steps;
    cin >> stairs_number >> jump_steps;


    long long pattern_count = 1; //all 1段上りは確定で1パータン存在する

    int iteration_number = stairs_number/jump_steps;

    for(int i = 1; i <= iteration_number;i++){
        int onestep_jump_num = stairs_number - jump_steps * i;
        init_nCk(i+onestep_jump_num);
        long long tmp = nCk(i+onestep_jump_num,i);

        pattern_count += tmp;
        
    }
    
    cout << pattern_count % MOD << endl;
    
}

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