//#define _GLIBCXX_DEBUG #include #define rep(i, n) for(int i=0; i; using vs = vector; using vi = vector; using vvi = vector; template using PQ = priority_queue; template using PQG = priority_queue, greater >; const int INF = 0xccccccc; const ll LINF = 0xcccccccccccccccLL; template inline bool chmax(T1 &a, T2 b) {return a < b && (a = b, true);} template inline bool chmin(T1 &a, T2 b) {return a > b && (a = b, true);} template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second;} template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second;} const unsigned int mod = 1000000007; //const unsigned int mod = 998244353; struct mint { unsigned int x; mint():x(0) {} mint(int64_t x_) { int64_t v = int64_t(x_ % mod); if(v < 0) v += mod; x = (unsigned int)v; } static mint row(int v) { mint v_; v_.x = v; return v_; } mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { uint64_t z = x; z *= a.x; x = (unsigned int)(z % mod); return *this; } mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} friend bool operator==(const mint &a, const mint &b) {return a.x == b.x;} friend bool operator!=(const mint &a, const mint &b) {return a.x != b.x;} mint &operator++() { x++; if(x == mod) x = 0; return *this; } mint &operator--() { if(x == 0) x = mod; x--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint pow(int64_t t) const { mint x_ = *this, r = 1; while(t) { if(t&1) r *= x_; x_ *= x_; t >>= 1; } return r; } //for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) {return mint(*this) /= a;} }; struct combination { vector frac, ifrac; combination(int n):frac(n+1), ifrac(n+1) { assert(n < mod); frac[0] = 1; for (int i = 1; i <= n; ++i) frac[i] = frac[i-1]*i; ifrac[n] = frac[n].inv(); for (int i = n; i >= 1; --i) ifrac[i-1] = ifrac[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return frac[n]*ifrac[k]*ifrac[n-k]; } } c(1000); istream& operator>>(istream& is, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} #define N 44 //head int n, m, k; P ab[N]; mint ans; int main() { ios::sync_with_stdio(false); cin.tie(0); cin >> n >> m >> k; rep(i, m) cin >> ab[i]; sort(ab, ab+m); rep(id, m) { vvi V; int cnt = 0; rep(i, m) { if(ab[i].second >= ab[id].second) { if(!V.empty() and ab[*V.back().begin()].first == ab[i].first) V.back().push_back(i); else V.push_back(vi(1, i)); cnt++; } } int u = V.size(); vector>> dp(u+1, vector>(cnt+1, vector(n+1))); rep(i, n+1) { dp[0][0][i] = mint(ab[*V.begin()->begin()].first).pow(n-i)*c(n, i); } cnt = 0; rep(i, u) { int z = V[i].size(); rep(j, cnt+1) rep(l, n+1) { rep(p, l+1) { int y = (i == u-1?k+1:ab[V[i+1][0]].first); if(y <= ab[id].first or j-p+z > 0) { dp[i+1][max(0, j-p+z)][l-p] += dp[i][j][l]*c(l, p)*mint(y-ab[V[i][0]].first).pow(p); } else break; } } cnt += z; } ans += mint(k+1).pow(n) * ab[id].second; rep(i, cnt+1) { ans -= dp[u][i][0] * ab[id].second; } } ans /= mint(k+1).pow(n); cout << ans << endl; }