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

#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

#ifdef LOCAL
auto operator<<(auto& o, auto x) -> decltype(x.first, o);
auto operator<<(auto& o, auto x) -> decltype(x.end(), o) {
  o << "{";
  for (int i = 0; auto y : x) o << ", " + !i++ * 2 << y;
  return o << "}"; }
auto operator<<(auto& o, auto x) -> decltype(x.first, o) {
  return o << "(" << x.first << ", " << x.second << ")"; }
void __print(auto... x) { ((cerr << x << " "), ...) << endl; }
#define debug(x...) __print("[" #x "]:", x)
#else
#define debug(...) 2137
#endif

template<int M, int R>
struct Mod {
  static const int mod = M, rt = R;
  int x;
  Mod(ll y = 0) : x(y % M) { x += (x < 0) * M; }
  Mod& operator+=(Mod o) {
    if ((x += o.x) >= M) x -= M;
    return *this; }
  Mod& operator-=(Mod o) {
    if ((x -= o.x) < 0) x += M;
    return *this; }
  Mod& operator*=(Mod o) {
    x = 1ll * x * o.x % M;
    return *this; }
  Mod& operator/=(Mod o) { return *this *= o.inv(); }
  friend Mod operator+(Mod a, Mod b) { return a += b; }
  friend Mod operator-(Mod a, Mod b) { return a -= b; }
  friend Mod operator*(Mod a, Mod b) { return a *= b; }
  friend Mod operator/(Mod a, Mod b) { return a /= b; }
  auto operator<=>(const Mod&) const = default;
  Mod pow(ll n) const {
    Mod a = x, b = 1;
    for (; n; n /= 2, a *= a) if (n % 2) b *= a;
    return b; }
  Mod inv() const { assert(x); return pow(M - 2); }
  friend ostream& operator<<(ostream& os, Mod x) {
    return os << x.x; }
};
using mint = Mod<1000000007, -1>;

int main() {
  cin.tie(0)->sync_with_stdio(0);

  int n, k, m;
  cin >> n >> k >> m;
  
  vector<mint> p(m), pre(m);
  p[0] = 1;
  for(int i = 1; i < m; i++) {
    pre[i] = pre[i - 1] + p[i - 1];
    p[i] = (pre[i] - pre[max(0, i - k)]) / k;
  }
  
  vector<mint> q(m), suf(m + 1);
  for(int i = m - 1; i >= max(m - k, 0); i--) {
    q[i] = 1 - (m - 1 - i) / mint(k);
    suf[i] = suf[i + 1] + q[i] * p[i];
  }
  
  mint ans = 0;
  for(int i = 0; i < m - k; i++) {
    ans += p[i];
  }
  ans *= n;
  
  for(int i = max(0, m - k); i < m; i++) {
    ans += (suf[i].pow(n) - suf[i + 1].pow(n)) / q[i];
  }
  
  cout << ans << endl;
}