#include #include using u32 = unsigned int; using u64 = unsigned long long int; /* \sum_{t=1}^inf [x^m] [(x+...+x^{k-1})]^t [y^{n-m}] [y/(1-y)]^{t-1} [1/(1-y)]^2 \sum_{t=1}^inf [x^m] [(x+...+x^{k-1})]^t [y^{n-m-t+1}] [1/(1-y)]^{t+1} \sum_{t=1}^inf [x^m] [(x+...+x^{k-1})]^t \binom{n-m+1}{t} [x^m] \sum_{t=1}^inf [(x+...+x^{k-1})]^t \binom{n-m+1}{t} [x^m] (1 + (x+...+x^{k-1}))^{n-m+1} [x^m] (1 + x(1-x^{k-1})/(1-x))^{n-m+1} [x^m] [(1-x^k) / (1-x)]^{n-m+1} \sum_{s=0}^{m/k} (-1)^s \binom{n-m+1}{s} \binom{m-sk + n-m}{n-m} \sum_{s=0}^{m/k} (-1)^s \binom{n-m+1}{s} \binom{n-sk}{n-m} \sum_{s=0}^{m/k} (-1)^s fact[n-m+1] * ifact[s] * ifact[n-m+1-s] * fact[n-sk] * ifact[n-m] * ifact[m-sk] \sum_{s=0}^{m/k} (-1)^s (n-m+1) * ifact[s] * ifact[n-m+1-s] * fact[n-sk] * ifact[m-sk] */ constexpr u32 mod = 998244353; u64 fact[10000001]; u64 ifact[10000001]; u32 binom(u32 n, u32 k){ return (u64) fact[n] * ifact[k] % mod * ifact[n-k] % mod; } u32 pw(u32 a, u32 n){ u32 r = 1; for(; n; n >>= 1){ if(n&1) r = (u64) r * a % mod; a = (u64) a * a % mod; } return r; } u32 inv(u32 a){ return pw(a, mod-2); } int main(){ u32 n, m, k; scanf("%d%d%d", &n, &m, &k); fact[0] = 1; for(int i = 1; i <= n; i++) fact[i] = fact[i-1] * i % mod; ifact[n] = inv(fact[n]); for(int i = n-1; i >= 0; i--) ifact[i] = (u64) (i+1) * ifact[i+1] % mod; u64 ans = 0; for(int i = 0; i <= std::min(m/k, n-m+1); i++){ if(i&1) ans += (u64) (mod-n+m-1) * ifact[i] % mod * ifact[n-m+1-i] % mod * fact[n-i*k] % mod * ifact[m-i*k] % mod; else ans += (u64) (n-m+1) * ifact[i] % mod * ifact[n-m+1-i] % mod * fact[n-i*k] % mod * ifact[m-i*k] % mod; } ans %= mod; printf("%lld\n", (mod + binom(n, m) - ans) % mod); return 0; }