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; } 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; enum LIM_INV = 4 * 10^^5 + 10; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM_INV]; fac = new Mint[LIM_INV]; invFac = new Mint[LIM_INV]; inv[1] = 1; foreach (i; 2 .. LIM_INV) { inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]); } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM_INV) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (n < 0) { if (k >= 0) { return (-1)^^(k & 1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (-1)^^((n - k) & 1) * binom(-k - 1, n - k); } else { return Mint(0); } } else { if (0 <= k && k <= n) { assert(n < LIM_INV); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } } int N, M; int[] A; Mint solve() { int L; int[] B, C; for (int i = 0, j; i < N; i = j) { for (j = i; j < N && A[i] == A[j]; ++j) {} B ~= A[i]; C ~= (j - i); } const K = cast(int)(B.length); debug { writefln("B = %s, C = %s", B, C); } Mint ans = 1; int sumL, sumR; auto ls = new int[K]; auto rs = new int[K]; foreach_reverse (k; 1 .. K) { const l = N - sumL - B[k]; const r = N - sumR - B[k]; if (l > 0 && r > 0 && C[k] == l && C[k] == r) { ans *= 2; ls[k] = l; } else if (l > 0 && r > 0 && C[k] == l + r) { ls[k] = l; rs[k] = r; } else if (l > 0 && C[k] == l) { ls[k] = l; } else if (r > 0 && C[k] == r) { rs[k] = r; } else { return Mint(0); } sumL += ls[k]; sumR += rs[k]; } debug { writefln("ls = %s, rs = %s", ls, rs); } { int l; foreach_reverse (k; 1 .. K) if (ls[k]) { if (max(l, N - ls[k] - l) != B[k]) { return Mint(0); } l += ls[k]; } } { int r; foreach_reverse (k; 1 .. K) if (rs[k]) { if (max(r, N - rs[k] - r) != B[k]) { return Mint(0); } r += rs[k]; } } if (max(sumL, sumR) != B[0]) { return Mint(0); } int cnt = 1; foreach (k; 1 .. K) { if (ls[k]) ++cnt; if (rs[k]) ++cnt; ans *= binom(C[k], ls[k]); } ans *= binom(M, cnt); return ans; } void main() { prepare; try { for (; ; ) { const numCases = readInt; foreach (caseId; 0 .. numCases) { N = readInt; M = readInt; A = new int[N]; foreach (i; 0 .. N) { A[i] = readInt; } A.sort; const ans = solve; writeln(ans); } } } catch (EOFException e) { } }