scenes2.cpp

/**
 *  @brief   Kattis - Mountain Scenes 
 *  @author  Donald Dong (@donaldong)
 *  @date    04/20/2018
 *  
 *  + DP
 */

#include <algorithm>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

typedef unsigned int uint;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
#define hmap unordered_map
#define hset unordered_set
#define pq priority_queue
#define pb push_back
#define mp make_pair
#define putchar putchar_unlocked
#define rep(i, s, e) for (size_t i = s, fe__ = e; i < fe__; ++i)

inline void scan(int&);
inline void scan(ll&);
inline void print(uint);
inline void print(ull);
inline void print(string&);

ll MOD = 1e9 + 7;

ll poss(int amt, int wid, int hgt, vector<vector<ll>> &used){
    if (wid == 0 || amt == 0) return 1;
    if (used[amt][wid] != -1) return used[amt][wid];
    ll count = 0;
    for (int i = 0; i <= hgt && i <= amt; ++i) {
        count += poss(amt - i, wid - 1, hgt, used);
        count %= MOD; 
    }
    used[amt][wid] = count;
    return count;
}

int main() {
    int amt, wid, hgt;
    cin >> amt >> wid >> hgt;
    vector<vector<ll>> used(amt + 1, vector<ll>(wid + 1, -1));
    ll ans = poss(amt, wid, hgt, used) - min(amt/hgt, hgt) - 1;
    if (ans < 0) ans += MOD;
    cout << ans << endl;
    return 0;
}

inline void scan(int &number) {
    bool negative = false;
    int c;
    number = 0;
    c = getchar();
    if (c=='-') {
        negative = true;
        c = getchar();
    }
    for (; (c>47 && c<58); c=getchar()) number = number *10 + c - 48;
    if (negative) number *= -1;
}

inline void scan(ll &number) {
    bool negative = false;
    int c;
    number = 0;
    c = getchar();
    if (c=='-') {
        negative = true;
        c = getchar();
    }
    for (; (c>47 && c<58); c=getchar()) number = number *10 + c - 48;
    if (negative) number *= -1;
}

inline void print(uint n) {
    if (n == 0) {
        putchar('0');
        return;
    }
    char buf[11];
    int i = 10;
    while (n) {
        buf[i--] = n % 10 + '0';
        n /= 10;
    }
    while (i < 10) putchar(buf[++i]);
}

inline void print(ull n) {
    if (n == 0) {
        putchar('0');
        return;
    }
    char buf[20];
    int i = 19;
    while (n) {
        buf[i--] = n % 10 + '0';
        n /= 10;
    }
    while (i < 19) putchar(buf[++i]);
}

inline void print(string &s) {
    rep(i, 0, s.length()) putchar(s[i]);
}