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 DATA = [ // M = 1, K = 0 [ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 1, K = 1 [ [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 2, K = 0 [ [0, 99824436, 299473304, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 299473306, -149736654, -249561090, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [399297734, -299473332, 299473278, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 2, K = 1 [ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 2, K = 2 [ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 3, K = 0 [ [0, -452287368, -180009503, -340239546, -49799024, 451586725, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -356246365, 288661955, -289344629, 52062632, -410213287, -258804093, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [56913184, 432346183, 379816413, -47679327, -23893675, 213029109, 184860043, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [50445436, -417796192, -486100547, 84253275, -366200244, 49295716, -480636199, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-108004946, 266028116, 449594855, 28781191, -215795466, 52817218, 221832082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 3, K = 1 [ [0, 175599997, 384770591, 433050330, 334966453, 99824429, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-429967448, -115860809, -411769635, -205215530, -134824600, -59155216, 73944020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-379184968, -139955191, -431165726, -178174768, 89225794, -107218836, 295776105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-243241409, -411946274, -474588732, 60386582, 284932316, -155282127, -73943994, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [123538026, 108170837, -204291439, 308963182, -56693167, 147887622, -295776132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 3, K = 2 [ [0, 421480952, 138645039, -169146948, -399297747, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8318703, 415935147, 133099245, -410389343, -399297736, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [30501912, -244939583, 203346064, -415935182, -303170543, -406692155, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-332747992, -55457453, 258805007, 240318763, 73944260, -184860035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-83186874, 180238952, 360477489, -457528502, -443664123, 110916042, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 3, K = 3 [ [0, -332748117, 166374057, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [166374059, -249561088, -166374062, -249561093, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [499122174, -415935155, -415935155, 499122174, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [332748151, -499122114, -83186994, -249561082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 4, K = 0 [ [0, -267755483, 369222961, 461808853, -359677444, 380132399, -180968798, 481046694, 20488741, 133099233, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 290332580, -246893316, 37958111, 393499767, -485841401, -409540381, -340251652, 25586736, -378111030, 206667773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-324024955, -241393270, 354558207, 376577624, -160539074, 130554452, -167057741, -139097408, 404987747, -361863744, -343146530, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-40940071, -405131450, -459578451, -132443626, 163518437, 364671601, -172543843, 484635922, 475529754, 106582812, 452329433, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [353411913, -29904769, -413175266, -214481388, 74430394, 242789619, -423448745, -115641853, -373952564, -291154229, 374341648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 4, K = 1 [ [0, -376898106, 386033059, -241867814, -27232042, -421942950, -369595720, -446975280, 39523102, 472152601, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11441204, -342702539, 45208975, 302133848, 315033095, 117997198, -407444841, -32551269, -399811741, -218561011, -42893321, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [381971063, 171851654, 285983487, -81717264, 493851606, 191937080, 238824083, 273931075, -197703680, 7423730, 358744069, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-81214863, 23816693, -60017311, 13710632, -342613658, -181506205, 487474379, -211030041, -330610701, -369711134, -397737901, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6865913, -349516168, -141907942, 178076525, 5687034, 128645675, 157679623, 450793957, 49601730, 184645967, -483524755, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [294442099, 25249615, -330215826, 275626860, 338201184, 93239136, -238037241, 484595663, -466323241, -465671324, -183271378, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 4, K = 2 [ [0, -366639318, -69284393, 76704069, -351437963, -292069379, 171721672, 464109903, 378787623, 442587288, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-454479503, 468184790, 325886306, 426995207, 322844807, 178601177, 200359545, -48057993, -334907033, -381805974, 144277498, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [257131165, 205394570, -233216577, -352099876, 18490531, 33348599, -392168194, 23061008, -387705556, 148303023, -202768398, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [162679376, -239655557, -308470474, 413857592, -172046772, 396928567, -338301251, 92128140, 163096156, 489241758, -350945241, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [61933628, -323283717, 356252651, -490370831, 27068249, 299530580, 79422468, 417972908, 46689557, 152797968, 483524708, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [405093067, -445565878, -204442100, 258856646, -214127619, 78884347, -399191508, 297438962, 251988587, 137130404, 487424054, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 4, K = 3 [ [0, -128366827, 12207843, 287616860, -474135891, 354736728, 323220409, -366746889, 153239251, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-161771485, 20661539, -106246779, 490570686, -215331626, 9355563, -382596086, -238864380, 444393912, 499122168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-402346446, 278590078, -245828103, -87202115, 111780264, 296349021, 263727921, -368001366, 18060353, -374341629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-206317533, 359893443, 106684951, -461551705, 257827755, -140005809, -73727011, 113427861, 227926982, 440631354, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [76591550, 156367248, -457907490, -412532278, 214414497, 276243057, 222157641, 335054072, -487801337, 210567115, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [487167407, 17375125, 229152361, -167361463, 2386004, 489011232, 72686873, -231821734, 333551824, 19496956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] , // M = 4, K = 4 [ [0, -291154604, -459839406, -258804106, 76254791, -166374065, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [101673036, -294235604, 443664155, 288073600, 46215023, -160212053, -258804097, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [110916040, 360477130, -358936645, 382044060, 16945405, -12324062, -36972025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-406692044, -237236650, 41594264, 146348210, -268046784, -172535986, 369720138, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [305021728, 443671398, 388984226, 15409330, 128633091, -486797971, 147888065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] ]; enum LIM = 6; enum DEG = 11; void main() { try { for (; ; ) { const N = readInt(); const M = readInt(); const K = readInt(); Mint r; foreach (k; -M .. +M + 1) { if (abs(k) != K) { r += 1; } } auto dp = new Mint[][LIM]; dp[0] = [Mint(1)]; foreach (i; 1 .. LIM) { dp[i] = new Mint[2 * M * i + 1]; foreach (j; 0 .. 2 * M * (i - 1) + 1) { foreach (k; -M .. +M + 1) { if (abs(k) != K) { dp[i][j + M + k] += dp[i - 1][j]; } } } } auto as = new Mint[LIM]; foreach (i; 0 .. LIM) { as[i] = dp[i][M * i]; } const data = DATA[M * (M + 1) / 2 - 1 + K]; const d = cast(int)(data.length) - 1; debug { writeln("================"); writefln("N = %s, M = %s, K = %s", N, M, K); writeln("as = ", as); writeln("data = ", data); } as.length = N + 1; foreach (i; LIM .. N + 1) { Mint numer; foreach (j; 1 .. d + 1) { Mint coef; foreach_reverse (c; data[j][0 .. DEG]) { (coef *= (i - j)) += c; } numer += coef * as[i - j]; } Mint denom; foreach_reverse (c; data[0][0 .. DEG]) { (denom *= i) += c; } as[i] = -numer / denom; } auto rr = new Mint[N + 1]; rr[0] = 1; foreach (i; 1 .. N + 1) { rr[i] = rr[i - 1] * r; } Mint ans; foreach (i; 0 .. N + 1) { ans += (N - i + 1) * rr[N - i] * (rr[i] - as[i]) / 2; } writeln(ans); } } catch (EOFException e) { } }