package contest210604; import java.io.*; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; public class G { InputStream is; FastWriter out; String INPUT = ""; public void solve() { int n = ni(), M = ni(), K = ni(); final int mod = 998244353; long[] dp = new long[2000]; int o = 1000; dp[o] = 1; long[] a = new long[200]; for(int i = 1;i <= 199;i++){ long[] ndp = new long[2000]; for(int j = 0;j < 2000;j++){ if(dp[j] == 0)continue; for(int l = -M;l <= M;l++){ if(l == -K || l == K)continue; ndp[j+l] += dp[j]; } } for(int j = 0;j < 2000;j++){ ndp[j] %= mod; } for(int j = 0;j < o;j++){ a[i] += ndp[j]; } a[i] %= mod; dp = ndp; } long[] hey = interpolate(n+1, mod, a); long ans = 0; int kk = 2*M+1 - (K == 0 ? 1 : 2); for(int len = 1;len <= n;len++){ ans += hey[len] * (n-len+1) % mod * pow(kk, n-len, mod); ans %= mod; } out.println(ans); } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } public static long[] interpolate(int n, int mod, long... base) { int m = base.length; long[][] res = guessLeaned(mod, base); return interpolate(res, Arrays.copyOf(base, n+1), m, n+1, mod); } public static long[][] guessLeaned(int mod, long... a) { int n = a.length; // #formula >= #variable // n-r+2 >= r(r+1)/2 for(int r = n;r >= 1;r--){ if(n-r+2 < r*(r+1)/2)continue; int[][] M = new int[n-r+2][r*(r+1)/2]; for(int i = 0;i < n-r+1;i++){ int p = 0; for(int j = 0;j < r;j++){ long prod = 1; for(int k = 0;k <= r-j-1;k++){ M[i][p++] = (int)(prod*a[i+j]%mod); prod = prod * i % mod; } } } M[n-r+1][0] = 1; int[] v = new int[n-r+2]; v[n-r+1] = 1; Result res = gaussElimination(M, v, mod); if(res.exists){ long[][] ret = new long[r][]; int p = 0; for(int i = 0;i < r;i++){ ret[i] = new long[r-i]; for(int j = 0;j < r-i;j++){ ret[i][j] = res.sol[p++]; } } // reformat int ilast = r; for(int i = r-1;i >= 0;i--){ int last = ret[i].length; while(last > 0 && ret[i][last-1] == 0)last--; ret[i] = Arrays.copyOf(ret[i], last); if(last == 0 && i+1 == ilast){ ilast--; } } ret = Arrays.copyOf(ret, ilast); return ret; } } return null; } public static Result gaussElimination(int[][] M, int[] v, int mod) { int n = M.length, m = M[0].length; int[] head = new int[n]; // if not needed, comment out. for(int[] row : M){ for(int i = 0;i < row.length;i++){ row[i] %= mod; if(row[i] < 0)row[i] += mod; } } // Forward Elimination int row = 0; for(int col = 0;col < m;col++){ // select pivot boolean pivotFound = false; out: for(int prow = row;prow < n;prow++){ if(M[prow][col] != 0){ // pivot found if(prow != row){ // swap rows for(int k = 0;k < m;k++){ int u = M[prow][k]; M[prow][k] = M[row][k]; M[row][k] = u; } int dum = v[prow]; v[prow] = v[row]; v[row] = dum; } pivotFound = true; break out; } } if(!pivotFound)continue; head[row] = col; // diag to 1 long imul = invl(M[row][col], mod); for(int k = 0;k < m;k++){ M[row][k] = (int)(M[row][k] * imul % mod); } v[row] = (int)(v[row] * imul % mod); for(int j = row+1;j < n;j++){ if(M[j][col] != 0){ long mul = mod-M[j][col]; for(int k = col;k < m;k++){ M[j][k] = (int)((M[j][k] + M[row][k] * mul) % mod); } v[j] = (int)((v[j] + v[row] * mul) % mod); } } row++; } Result ret = new Result(); ret.mat = M; for(int i = row;i < n;i++){ if(v[i] != 0){ ret.rank = row; ret.exists = false; return ret; } } for(int i = row-1;i >= 0;i--){ for(int j = i-1;j >= 0;j--){ if(M[j][head[i]] != 0){ long mul = mod-M[j][head[i]]; for(int k = head[i];k < m;k++){ M[j][k] = (int)((M[j][k] + M[i][k] * mul) % mod); } v[j] = (int)((v[j] + v[i] * mul) % mod); } } } int[] retv = new int[m]; for(int i = 0;i < row;i++){ retv[head[i]] = v[i]; } ret.sol = retv; ret.rank = row; ret.exists = true; return ret; } public static class Result { public int[][] mat; public int[] sol; public int rank; public boolean exists; } /** * vals[0,x-1]の情報を利用してvals[x]を埋める * @param ged * @param vals * @param x * @param mod */ public static long[] interpolate(long[][] ged, long[] vals, int l, int r, int mod) { int n = ged.length; for(int x = l, xx = x-(n-1);x < r;x++, xx++){ int pos = x; long s = 0; long tar = 0; for(int i = 0;i < n;i++){ long co = 0; for(int j = ged[i].length-1;j >= 0;j--){ co = (co * xx + ged[i][j]) % mod; } if(i < n-1){ s += co * vals[i+xx]; s %= mod; }else{ tar = co; } } long ret = (mod-invl(tar, mod)) * s % mod; vals[pos] = ret; } return vals; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static void main(String[] args) { new G().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(IntUnaryOperator f, int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(f.applyAsInt(x)); } return this; } public FastWriter write(LongUnaryOperator f, long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(f.applyAsLong(x)); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); } public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); } public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); } public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }