#include #include #include #include using namespace std; const int MOD = 1000000007; using LL = long long; class mint { LL val; mint& normalize(LL x) { val = x % MOD; if (val < 0) { val += MOD; } return *this; } static LL inverse(LL a) { LL u = 0, v = 1, m = MOD; while (a != 0) { LL t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u; } public: mint(LL x = 0) { normalize(x); } LL operator()() const { return val; } template explicit operator U() const { return static_cast(val); } mint& operator=(LL x) { return normalize(x); } mint& operator=(const mint& x) { val = x.val; return *this; } mint& operator+=(const mint& x) { return normalize(val + x.val); } mint& operator-=(const mint& x) { return normalize(val - x.val); } mint& operator*=(const mint& x) { return normalize(val * x.val); } mint& operator/=(const mint& x) { return *this *= mint(inverse(x.val)); } mint& operator+=(LL x) { return *this += mint(x); } mint& operator-=(LL x) { return *this -= mint(x); } mint& operator*=(LL x) { return *this *= mint(x); } mint& operator/=(LL x) { return *this /= mint(x); } mint& operator++() { return *this += 1; } mint& operator--() { return *this -= 1; } mint operator++(int) { mint z(*this); ++*this; return z; } mint operator--(int) { mint z(*this); --*this; return z; } friend mint operator+(mint x, const mint& y) { return x += y; } friend mint operator*(mint x, const mint& y) { return x *= y; } friend mint operator-(mint x, const mint& y) { return x -= y; } friend mint operator/(mint x, const mint& y) { return x /= y; } friend mint operator+(mint x, LL y) { return x += y; } friend mint operator*(mint x, LL y) { return x *= y; } friend mint operator-(mint x, LL y) { return x -= y; } friend mint operator/(mint x, LL y) { return x /= y; } friend mint operator+(LL x, mint y) { return y += x; } friend mint operator*(LL x, mint y) { return y *= x; } friend mint operator-(LL x, const mint& y) { mint z(x); return z -= y; } friend mint operator/(LL x, const mint& y) { mint z(x); return z /= y; } bool operator <(const mint& x) const { return val < x.val; } bool operator==(const mint& x) const { return val == x.val; } bool operator >(const mint& x) const { return val > x.val; } bool operator!=(const mint& x) const { return val != x.val; } bool operator<=(const mint& x) const { return val <= x.val; } bool operator>=(const mint& x) const { return val >= x.val; } bool operator <(LL x) const { return val < x; } bool operator==(LL x) const { return val == x; } bool operator >(LL x) const { return val > x; } bool operator!=(LL x) const { return val != x; } bool operator<=(LL x) const { return val <= x; } bool operator>=(LL x) const { return val >= x; } }; class factorial : vector { void lazy_eval(int n) { for (LL p = size(); n >= p; ++p) { push_back(back() * p); } } public: factorial() { push_back(1); } mint choose(LL n, LL k) { if (n < 0 || k < 0 || n < k) { return 0; } if (k == 0 || k == n) { return 1; } if (n >= MOD && n <= k + MOD - 1) { return 0; } lazy_eval(n); return at(n) / (at(k) * at(n - k)); } mint operator[](LL n) { lazy_eval(n); return at(n); } }; factorial F; LL solve() { int N, K, c0, w0; cin >> N >> K >> c0 >> w0; LL lighter = 0, equal = 0, heavier = 0; for (int i = 1, c, w; i < N; i++) { cin >> c >> w; if (w < w0) { lighter += c; } else if (w == w0) { equal += c; } else { heavier += c; } } LL total = c0 + lighter + equal + heavier; LL not_heavier = total - heavier; K++; mint ways_some_equal = F.choose(not_heavier, K) - F.choose(lighter, K); mint prob_some_equal = ways_some_equal / F.choose(total, K); return LL(prob_some_equal * c0 / (c0 + equal)); } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }