1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

constexpr int mod = 1000000007;

int n, k, m;

vector<vector<int>> states;

// source: https://stackoverflow.com/questions/20511347/a-good-hash-function-for-a-vector
class vector_hasher {
public:
    std::size_t operator()(std::vector<int> const& vec) const {
        std::size_t seed = vec.size();
        for(auto& i : vec) {
            seed ^= i + 0x9e3779b9 + (seed << 6) + (seed >> 2);
        }
        return seed;
    }
};

long long modPow(long long a, long long b)
{
    if (b == 0) return 1;

    long long v = modPow(a, b / 2);
    v = (v * v) % mod;

    if (b & 1) return (v * a) % mod;
    else return v;
}

void dfs(vector<int> current)
{
    if (current.size() == n)
    {
        states.push_back(current);
        return;
    }

    for (int i : current)
    {
        if (i >= m) return;
    }

    int start = 0;
    if (!current.empty()) start = current.back();
    for (int i = start; i < k + m; ++i)
    {
        current.push_back(i);
        dfs(current);
        current.pop_back();
    }
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    cin >> n >> k >> m;

    dfs({});

    sort(states.begin(), states.end());

    cc_hash_table<vector<int>, long long, vector_hasher> dp1, dp2;

    long long answer = 0;

    dp2[states.front()] = 1;

    long long kInv = modPow(k, mod - 2);

    for (auto state : states)
    {
        if (state.back() >= m)
        {
            answer = (answer + dp1[state]) % mod;
            continue;
        }

        for (int i = 1; i <= k; ++i)
        {
            int v = state[0];
            vector<int> nextState = state;
            nextState.erase(nextState.begin());
            for (int j = 0; j <= nextState.size(); ++j)
            {
                if (j == nextState.size() || nextState[j] > v + i)
                {
                    nextState.insert(nextState.begin() + j, v + i);
                    break;
                }
            }

            long long v1 = (dp1[state] + dp2[state]) % mod;
            v1 = (v1 * kInv) % mod;

            long long v2 = (dp2[state] * kInv) % mod;

            dp1[nextState] = (dp1[nextState] + v1) % mod;
            dp2[nextState] = (dp2[nextState] + v2) % mod;
        }
    }

    cout << answer << '\n';
}