def II() -> int : return int(input()) def MI() -> int : return map(int, input().split()) def TI() -> tuple[int] : return tuple(MI()) def LI() -> list[int] : return list(MI()) class fenwick_tree(): n=1 data=[0 for i in range(n)] def __init__(self,N): self.n=N self.data=[0 for i in range(N)] def add(self,p,x): assert 0<=p0): s+=self.data[r-1] r-=r&-r return s """使われるであろうmod""" MOD = 998244353 """擬似的な虚数単位""" _IMAG = 911660635 _IIMAG = 86583718 """数論変換における回転因子の前計算""" _rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0) _irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0) _rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0) _irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0) def _fft(a): n = len(a) h = (n - 1).bit_length() le = 0 for le in range(0, h - 1, 2): p = 1 << (h - le - 2) rot = 1 for s in range(1 << le): rot2 = rot * rot % MOD rot3 = rot2 * rot % MOD offset = s << (h - le) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] * rot a2 = a[i + offset + p * 2] * rot2 a3 = a[i + offset + p * 3] * rot3 a1na3imag = (a1 - a3) % MOD * _IMAG a[i + offset] = (a0 + a2 + a1 + a3) % MOD a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD rot = rot * _rate3[(~s & -~s).bit_length()] % MOD if h - le & 1: rot = 1 for s in range(1 << (h - 1)): offset = s << 1 l = a[offset] r = a[offset + 1] * rot a[offset] = (l + r) % MOD a[offset + 1] = (l - r) % MOD rot = rot * _rate2[(~s & -~s).bit_length()] % MOD def _ifft(a): n = len(a) h = (n - 1).bit_length() le = h for le in range(h, 1, -2): p = 1 << (h - le) irot = 1 for s in range(1 << (le - 2)): irot2 = irot * irot % MOD irot3 = irot2 * irot % MOD offset = s << (h - le + 2) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] a2 = a[i + offset + p * 2] a3 = a[i + offset + p * 3] a2na3iimag = (a2 - a3) * _IIMAG % MOD a[i + offset] = (a0 + a1 + a2 + a3) % MOD a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD irot = irot * _irate3[(~s & -~s).bit_length()] % MOD if le & 1: p = 1 << (h - 1) for i in range(p): l = a[i] r = a[i + p] a[i] = l + r if l + r < MOD else l + r - MOD a[i + p] = l - r if l - r >= 0 else l - r + MOD def ntt(a) -> None: if len(a) <= 1: return _fft(a) def intt(a) -> None: if len(a) <= 1: return _ifft(a) iv = pow(len(a), MOD - 2, MOD) for i, x in enumerate(a): a[i] = x * iv % MOD def multiply(s: list, t: list) -> list: n, m = len(s), len(t) l = n + m - 1 if min(n, m) <= 60: a = [0] * l for i, x in enumerate(s): for j, y in enumerate(t): a[i + j] += x * y return [x % MOD for x in a] z = 1 << (l - 1).bit_length() a = s + [0] * (z - n) b = t + [0] * (z - m) _fft(a) _fft(b) for i, x in enumerate(b): a[i] = a[i] * x % MOD _ifft(a) a[l:] = [] iz = pow(z, MOD - 2, MOD) return [x * iz % MOD for x in a] mod = 998244353 q = II() const = 4000 ans = [0]*q qry = [[] for i in range(const+1)] for i in range(q): t,n,k = MI() if k == 1: ans[i] = 1 qry[k].append((i,n)) dp = [1]*(const+1) for d in range(2,const+1): a = [0]*(const+1) for j in range(0,const+1,d): a[j] = 1 dp = multiply(dp,a)[:const+1] for i,n in qry[d]: ans[i] = dp[n] for i in ans: print(i)