import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(int M_) { import std.conv : to; alias M = M_; int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { if (a < 0) return (this = inv()^^(-a)); ModInt t2 = this, te = ModInt(1); for (long e = a; e > 0; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op: "-")() const { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; enum LIM = 2 * 10^^5; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM]; fac = new Mint[LIM]; invFac = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)]; } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } // M: prime, G: primitive root class Fft(int M_, int G, int K) { import std.algorithm : reverse; import std.traits : isIntegral; alias M = M_; // 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ... int[] gs; this() { static assert(2 <= K && K <= 30, "Fft: 2 <= K <= 30 must hold"); static assert(!((M - 1) & ((1 << K) - 1)), "Fft: 2^K | M - 1 must hold"); gs = new int[1 << (K - 1)]; gs[0] = 1; long g2 = G, gg = 1; for (int e = (M - 1) >> K; e; e >>= 1) { if (e & 1) gg = (gg * g2) % M; g2 = (g2 * g2) % M; } gs[1 << (K - 2)] = cast(int)(gg); for (int l = 1 << (K - 2); l >= 2; l >>= 1) { gs[l >> 1] = cast(int)((cast(long)(gs[l]) * gs[l]) % M); } assert((cast(long)(gs[1]) * gs[1]) % M == M - 1, "Fft: g^(2^(K-1)) == -1 (mod M) must hold"); for (int l = 2; l <= 1 << (K - 2); l <<= 1) { foreach (i; 1 .. l) { gs[l + i] = cast(int)((cast(long)(gs[l]) * gs[i]) % M); } } } void fft(int[] xs) const { const n = cast(int)(xs.length); assert(!(n & (n - 1)), "Fft.fft: |xs| must be a power of two"); assert(n <= 1 << K, "Fft.fft: |xs| <= 2^K must hold"); for (int l = n; l >>= 1; ) { foreach (i; 0 .. (n >> 1) / l) { const(long) g = gs[i]; foreach (j; (i << 1) * l .. (i << 1 | 1) * l) { const t = cast(int)((g * xs[j + l]) % M); if ((xs[j + l] = xs[j] - t) < 0) xs[j + l] += M; if ((xs[j] += t) >= M) xs[j] -= M; } } } } void invFft(int[] xs) const { const n = cast(int)(xs.length); assert(!(n & (n - 1)), "Fft.invFft: |xs| must be a power of two"); assert(n <= 1 << K, "Fft.invFft: |xs| <= 2^K must hold"); for (int l = 1; l < n; l <<= 1) reverse(xs[l .. l << 1]); for (int l = 1; l < n; l <<= 1) { foreach (i; 0 .. (n >> 1) / l) { const(long) g = gs[i]; foreach (j; (i << 1) * l .. (i << 1 | 1) * l) { int t = cast(int)((g * (xs[j] - xs[j + l])) % M); if (t < 0) t += M; if ((xs[j] += xs[j + l]) >= M) xs[j] -= M; xs[j + l] = t; } } } } T[] convolute(T)(inout(T)[] as, inout(T)[] bs) const if (isIntegral!T) { const na = cast(int)(as.length), nb = cast(int)(bs.length); int n, invN = 1; for (n = 1; n < na + nb - 1; n <<= 1) { invN = ((invN & 1) ? (invN + M) : invN) >> 1; } auto xs = new int[n], ys = new int[n]; foreach (i; 0 .. na) if ((xs[i] = cast(int)(as[i] % M)) < 0) xs[i] += M; foreach (i; 0 .. nb) if ((ys[i] = cast(int)(bs[i] % M)) < 0) ys[i] += M; fft(xs); fft(ys); foreach (i; 0 .. n) { xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M); } invFft(xs); auto cs = new T[na + nb - 1]; foreach (i; 0 .. na + nb - 1) cs[i] = cast(T)(xs[i]); return cs; } ModInt!M[] convolute(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) const { const na = cast(int)(as.length), nb = cast(int)(bs.length); int n, invN = 1; for (n = 1; n < na + nb - 1; n <<= 1) { invN = ((invN & 1) ? (invN + M) : invN) >> 1; } auto xs = new int[n], ys = new int[n]; foreach (i; 0 .. na) xs[i] = as[i].x; foreach (i; 0 .. nb) ys[i] = bs[i].x; fft(xs); fft(ys); foreach (i; 0 .. n) { xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M); } invFft(xs); auto cs = new ModInt!M[na + nb - 1]; foreach (i; 0 .. na + nb - 1) cs[i].x = xs[i]; return cs; } int[] convolute(int M1)(inout(ModInt!M1)[] as, inout(ModInt!M1)[] bs) const if (M != M1) { const na = cast(int)(as.length), nb = cast(int)(bs.length); int n, invN = 1; for (n = 1; n < na + nb - 1; n <<= 1) { invN = ((invN & 1) ? (invN + M) : invN) >> 1; } auto xs = new int[n], ys = new int[n]; foreach (i; 0 .. na) xs[i] = as[i].x; foreach (i; 0 .. nb) ys[i] = bs[i].x; fft(xs); fft(ys); foreach (i; 0 .. n) { xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M); } invFft(xs); return xs[0 .. na + nb - 1]; } ModInt!M[] square(inout(ModInt!M)[] as) const { const na = cast(int)(as.length); int n, invN = 1; for (n = 1; n < na + na - 1; n <<= 1) { invN = ((invN & 1) ? (invN + M) : invN) >> 1; } auto xs = new int[n]; foreach (i; 0 .. na) xs[i] = as[i].x; fft(xs); foreach (i; 0 .. n) { xs[i] = cast(int)((((cast(long)(xs[i]) * xs[i]) % M) * invN) % M); } invFft(xs); auto cs = new ModInt!M[na + na - 1]; foreach (i; 0 .. na + na - 1) cs[i].x = xs[i]; return cs; } } alias Fft0 = Fft!(998244353, 3, 20); void main() { prepare; const fft = new Fft0; try { for (; ; ) { const N = readInt(); const M = readInt(); const K = readInt(); // \sum_{a=K}^\infty S(a, K) x^a/a! = (1/K!) (e^x - 1)^K auto fs = new Mint[N - K + 1]; fs[0 .. N - K + 1] = invFac[1 .. N - K + 1 + 1]; auto gs = new Mint[N - K + 1]; gs[0] = 1; for (long e = K; e; e >>= 1) { if (e & 1) { gs = fft.convolute(gs, fs); gs.length = N - K + 1; } fs = fft.square(fs); fs.length = N - K + 1; } // \sum_{a=K}^N binom(N, a) binom(M, K) K! S(a, K) M^(N-a) auto mm = new Mint[N + 1]; mm[0] = 1; foreach (i; 1 .. N + 1) { mm[i] = mm[i - 1] * M; } Mint ans; foreach (a; K .. N + 1) { Mint prod = 1; prod *= fac[N]; prod *= invFac[N - a]; prod *= gs[a - K]; prod *= mm[N - a]; ans += prod; } ans *= binom(M, K); writeln(ans); } } catch (EOFException e) { } }