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; } string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; } 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(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = cast(uint)(x_ % M); } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; // x^e mod rev(cs) Mint[] powerRev(const(Mint[]) cs, long e) { assert(!cs.empty); assert(cs[0].x == 1); const d = cast(int)(cs.length) - 1; if (d == 0) { return []; } else if (d == 1) { return [(-cs[1])^^e]; } Mint[] mul(const(Mint[]) fs, const(Mint[]) gs) { auto hs = new Mint[d + d - 1]; foreach (i; 0 .. d) foreach (j; 0 .. d) { hs[i + j] += fs[i] * gs[j]; } foreach_reverse (i; d .. d + d - 1) { foreach (j; 1 .. d + 1) { hs[i - j] -= cs[j] * hs[i]; } } hs.length = d; return hs; } auto xs = new Mint[d]; auto ys = new Mint[d]; xs[1] = 1; ys[0] = 1; for (; ; xs = mul(xs, xs)) { if (e & 1) ys = mul(ys, xs); if (!(e >>= 1)) break; } return ys; } Mint linearRecurrenceAt(const(Mint[]) as, const(Mint[]) cs, long e) { assert(!cs.empty); assert(cs[0].x == 1); const d = cast(int)(cs.length) - 1; assert(as.length >= d); const fs = powerRev(cs, e); Mint ans; foreach (i; 0 .. d) { ans += fs[i] * as[i]; } return ans; } // square matrix Mint[][] mul(Mint[][] a, Mint[][] b) { const size = cast(int)(a.length); auto c = new Mint[][](size, size); foreach (i; 0 .. size) foreach (k; 0 .. size) foreach (j; 0 .. size) { c[i][j] += a[i][k] * b[k][j]; } return c; } Mint[] mul(Mint[][] a, Mint[] x) { const size = cast(int)(a.length); auto y = new Mint[size]; foreach (i; 0 .. size) foreach (j; 0 .. size) { y[i] += a[i][j] * x[j]; } return y; } Mint[][] power(Mint[][] a, long e) { const size = cast(int)(a.length); auto b = new Mint[][](size, size), c = new Mint[][](size, size); foreach (i; 0 .. size) foreach (j; 0 .. size) b[i][j] = a[i][j]; foreach (i; 0 .. size) foreach (j; 0 .. size) c[i][j] = (i == j) ? 1 : 0; for (; e; e >>= 1) { if (e & 1) c = mul(c, b); b = mul(b, b); } return c; } enum D = 6; Mint[] A, C; // [x^n] (1 - (x^1+...+x^D))^-1 Mint calc(long n) { return (n >= 0) ? linearRecurrenceAt(A, C, n) : Mint(0); } void main() { A = new Mint[D]; A[0] = 1; foreach (n; 1 .. D) { A[n] = 2^^(n-1); } C = new Mint[D + 1]; C[0] = 1; C[1 .. D + 1] = Mint(-1); debug { writeln(iota(20).map!(n => calc(n))); } try { for (; ; ) { const N = readLong; const M = readLong; const Q = readInt; Mint all; foreach (x; 1 .. D + 1) { all += calc(M * N - x) * (D + 1 - x); } debug { writeln("all = ", all); } auto a = new Mint[][](D - 1, D - 1); foreach (x; 1 .. D) foreach (y; 1 .. D) { // (C+mN)+x --> (C+(m+1)N)-y -> (C+(m+1)N)+z const way = calc((N-y) - x); foreach (z; 1 .. D) if (y + z <= D) { a[x - 1][z - 1] += way; } } a = a.power(M - 1); foreach (q; 0 .. Q) { const C = readLong; auto fs = new Mint[D - 1]; foreach (x; 1 .. D) foreach (y; 1 .. D) if (x + y <= D) { // 0 --> C-x -> C+y -...-> (C+(M-1)N)+z const way = calc(C-x); foreach (z; 1 .. D) { fs[z - 1] += way * a[y - 1][z - 1]; } } Mint ans; foreach (z; 1 .. D) { if (C + z >= N) { ans += fs[z - 1]; } else { // C+z --> N-w -> (>=N) foreach (w; 1 .. D + 1) { ans += fs[z - 1] * calc((N-w) - (C+z)) * (D + 1 - w); } } } debug { writefln("C = %s: fs = %s, ans = %s", C, fs, ans); } ans = all - ans; writeln(ans); } } } catch (EOFException e) { } }