//#pragma GCC optimize("Ofast") //#pragma GCC target("avx") //#undef LOCAL #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template using V = vector; template using VV = V>; #include struct Scanner { int fd = -1; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += ::read(fd, line + ed, (1 << 15) - ed); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template ::value, int> = 0> bool read_single(T& ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template ::value>* = nullptr> bool read_single(T& ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template bool read_single(V& ref) { for (auto& d : ref) { if (!read_single(d)) return false; } return true; } void read() {} template void read(H& h, T&... t) { bool f = read_single(h); assert(f); read(t...); } int read_unsafe() { return 0; } template int read_unsafe(H& h, T&... t) { bool f = read_single(h); if (!f) return 0; return 1 + read_unsafe(t...); } Scanner(FILE* fp) : fd(fileno(fp)) {} }; struct Printer { public: template void write() {} template void write(const H& h, const T&... t) { if (F) write_single(' '); write_single(h); write(t...); } template void writeln(const T&... t) { write(t...); write_single('\n'); } Printer(FILE* _fp) : fp(_fp) {} ~Printer() { flush(); } private: static constexpr size_t SIZE = 1 << 15; FILE* fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write_single(const char& val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value>* = nullptr> void write_single(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write_single('0'); return; } if (val < 0) { write_single('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write_single(__int128 val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write_single('0'); return; } if (val < 0) { write_single('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write_single(const string& s) { for (char c : s) write_single(c); } void write_single(const char* s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write_single(s[i]); } template void write_single(const V& val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write_single(' '); write_single(val[i]); } } }; template struct ModInt { using M = ModInt; static constexpr uint get_mod() { return MD; } const static M G; uint v; ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); } M& set_v(uint _v) { v = (_v < MD) ? _v : _v - MD; return *this; } explicit operator bool() const { return v != 0; } M operator-() const { return M() - *this; } M operator+(const M& r) const { return M().set_v(v + r.v); } M operator-(const M& r) const { return M().set_v(v + MD - r.v); } M operator*(const M& r) const { return M().set_v(uint(ull(v) * r.v % MD)); } M operator/(const M& r) const { return *this * r.inv(); } M& operator+=(const M& r) { return *this = *this + r; } M& operator-=(const M& r) { return *this = *this - r; } M& operator*=(const M& r) { return *this = *this * r; } M& operator/=(const M& r) { return *this = *this / r; } bool operator==(const M& r) const { return v == r.v; } M pow(ll n) const { M x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } M inv() const { return pow(MD - 2); } friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; } }; // using Mint = ModInt<998244353>; // template<> const Mint Mint::G = Mint(3); template V powTable(int n, Mint x) { V table(n + 1); table[0] = Mint(1); for (int i = 1; i <= n; i++) { table[i] = table[i - 1] * x; } return table; } template struct Comb { int max_n; V fact, ifact; Comb() {} Comb(int n) : max_n(n) { fact = ifact = V(n + 1); fact[0] = Mint(1); for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; i--) ifact[i - 1] = ifact[i] * i; } Mint C(int n, int k) { if (n < k || n < 0) return Mint(0); assert(0 <= k && k <= n && n <= max_n); return fact[n] * ifact[k] * ifact[n - k]; } // n個の区別出来ないボールをk個の箱に入れる入れ方 Mint H(int n, int k) { if (n == 0 && k == 0) return Mint(1); return C(n + k - 1, n); } }; using Mint = ModInt; Comb C(100); Scanner sc = Scanner(stdin); Printer pr = Printer(stdout); // (残った人数, lw, mid, up) Mint dp[42][42][2][42]; Mint ndp[42][42][2][42]; void succ() { for (int i = 0; i < 42; i++) { for (int j = 0; j < 42; j++) { for (int k = 0; k < 2; k++) { for (int l = 0; l < 42; l++) { dp[i][j][k][l] = ndp[i][j][k][l]; ndp[i][j][k][l] = Mint(0); } } } } } int main() { int n, m, pri; sc.read(n, m, pri); using P = pair; V

vs(m + 1); vs[0] = P(0, 0); for (int i = 1; i <= m; i++) { sc.read(vs[i].first, vs[i].second); } m++; sort(vs.begin(), vs.end()); int bk = pri + 1; for (int i = m - 1; i >= 0; i--) { auto buf = vs[i].first; vs[i].first = bk - vs[i].first; bk = buf; } Mint ans = 0; for (int trg = 0; trg < m; trg++) { P tp = P(vs[trg].second, trg); succ(); succ(); dp[n][0][0][0] = 1; int now_j = 0, now_l = 0; for (int ph = 0; ph < m; ph++) { P now_p = P(vs[ph].second, ph); // inc object for (int i = 0; i <= n; i++) { for (int j = 0; j <= now_j; j++) { for (int k = 0; k < 2; k++) { for (int l = 0; l <= now_l; l++) { if (!dp[i][j][k][l].v) continue; int nj = j; int nk = k; int nl = l; if (tp > now_p) nj++; if (tp == now_p) nk++; if (tp < now_p) nl++; ndp[i][nj][nk][nl] += dp[i][j][k][l]; } } } } if (tp > now_p) now_j++; if (tp < now_p) now_l++; succ(); Mint b = vs[ph].first; // inc human for (int i = 0; i <= n; i++) { for (int w = 0; w <= i; w++) { Mint freq = C.C(i, w) * b.pow(w); for (int j = 0; j <= now_j; j++) { for (int k = 0; k < 2; k++) { for (int l = 0; l <= now_l; l++) { if (!dp[i][j][k][l].v) continue; int z = w; int nl = l - min(l, z); z -= l - nl; int nk = k - min(k, z); z -= k - nk; int nj = j - min(j, z); z -= j - nj; ndp[i - w][nj][nk][nl] += dp[i][j][k][l] * freq; } } } } } succ(); } Mint sum = 0; for (int j = 0; j < 42; j++) { for (int l = 0; l < 42; l++) { sum += dp[0][j][0][l]; } } ; ans += sum * vs[trg].second; } ; ans /= Mint(pri + 1).pow(n); pr.writeln(ans.v); return 0; }