#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m = mod) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1000; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } int gcd(int a, int b) { if (a < b)swap(a, b); while (b) { int r = a % b; a = b; b = r; } return a; } //見てる場所,残り個数,必要個数 modint dp[50][50][50]; void solve() { int n, m, k; cin >> n >> m >> k; vector a(m), b(m); rep(i, m)cin >> a[i] >> b[i]; { auto comp = [&](int i, int j)->bool { return b[i] > b[j]; }; vector ori(m); rep(i, m)ori[i] = i; sort(all(ori), comp); vector ca = a, cb = b; rep(i, m) { a[i] = ca[ori[i]]; b[i] = cb[ori[i]]; } //rep(i, m)cout << "! " << a[i] << " " << b[i] << "\n"; } modint ans = 0; rep(i, m) { vector locs; locs.push_back(k + 1); rep(j, i + 1) { locs.push_back(a[j]); } sort(all(locs)); int sta = lower_bound(all(locs), a[i]) - locs.begin(); int el = k + 1; modint csum = 0; rep(j, 50)rep(k, 50)rep(l,50)dp[j][k][l] = 0; dp[0][n][0] = 1; rep(j, locs.size() - 1) { int dif = locs[j + 1] - locs[j]; rep(k, n + 1) { rep(l, j+1) { for (int num = 0; num <= k; num++) { modint c = comb(k,num) * (modint)mod_pow(dif, num); c *= dp[j][k][l]; if (j < sta) { dp[j + 1][k - num][max(0, l + 1 - num)] += c; } else { if (l + 1 - num <= 0) { csum += c * (modint)mod_pow(el - dif, k-num); } else { dp[j + 1][k - num][l + 1 - num] += c; } } } } } el -= dif; } //cout << "valid\n"; //cout << dp[1][0] << " " << dp[1][1] << "\n"; //cout << i << " " << csum << "\n"; ans += csum * (modint)b[i]; } ans = ans / (modint)mod_pow(k + 1, n); cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(15); init_f(); //init(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }