#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp" #define _CRT_SECURE_NO_WARNINGS #pragma target("avx2") #pragma optimize("O3") #pragma optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i,n) for(int i=0;i<(n);i++) #define REP(i,n) for(int i=1;i<=(n);i++) #define all(V) V.begin(),V.end() typedef unsigned int uint; typedef long long lint; typedef unsigned long long ulint; typedef std::pair P; typedef std::pair LP; constexpr int INF = INT_MAX/2; constexpr lint LINF = LLONG_MAX/2; constexpr double eps = DBL_EPSILON; constexpr double PI=3.141592653589793238462643383279; template class prique :public std::priority_queue, std::greater> {}; template inline bool chmax(T& lhs, const U& rhs) { if (lhs < rhs) { lhs = rhs; return 1; } return 0; } template inline bool chmin(T& lhs, const U& rhs) { if (lhs > rhs) { lhs = rhs; return 1; } return 0; } inline lint gcd(lint a, lint b) { while (b) { lint c = a; a = b; b = c % b; } return a; } inline lint lcm(lint a, lint b) { return a / gcd(a, b) * b; } bool isprime(lint n) { if (n == 1)return false; for (int i = 2; i * i <= n; i++) { if (n % i == 0)return false; } return true; } template T mypow(T a, lint b) { T res(1); while(b){ if(b&1)res*=a; a*=a; b>>=1; } return res; } lint modpow(lint a, lint b, lint m) { lint res(1); while(b){ if(b&1){ res*=a;res%=m; } a*=a;a%=m; b>>=1; } return res; } template void printArray(std::vector& vec) { rep(i, vec.size()){ std::cout << vec[i]; std::cout<<(i==(int)vec.size()-1?"\n":" "); } } template void printArray(T l, T r) { T rprev = std::prev(r); for (T i = l; i != rprev; i++) { std::cout << *i << " "; } std::cout << *rprev << std::endl; } LP extGcd(lint a,lint b) { if(b==0)return {1,0}; LP s=extGcd(b,a%b); std::swap(s.first,s.second); s.second-=a/b*s.first; return s; } LP ChineseRem(const lint& b1,const lint& m1,const lint& b2,const lint& m2) { lint p=extGcd(m1,m2).first; lint tmp=(b2-b1)*p%m2; lint r=(b1+m1*tmp+m1*m2)%(m1*m2); return std::make_pair(r,m1*m2); } template inline constexpr decltype(auto) lambda_fix(F&& f){ return [f=std::forward(f)](auto&&... args){ return f(f,std::forward(args)...); }; } #line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/algebraic/ModInt.hpp" class ModInt { lint value; public: constexpr static unsigned int modulo = 1000000007; ModInt() : value(0) {} template ModInt(T value = 0) : value(value) { if (value < 0)value = -(lint)(-value % modulo) + modulo; this->value = value % modulo; } inline ModInt inv()const{return mypow(*this,modulo-2);} inline operator int()const { return value; } inline ModInt& operator+=(const ModInt& x) { value += x.value; if (value >= modulo)value -= modulo; return *this; } inline ModInt& operator++() { if (value == modulo - 1)value = 0; else value++; return *this; } inline ModInt operator-()const { return ModInt(0) -= *this; } inline ModInt& operator-=(const ModInt& x) { value -= x.value; if (value < 0)value += modulo; return *this; } inline ModInt& operator--() { if (value == 0)value = modulo - 1; else value--; return *this; } inline ModInt& operator*=(const ModInt& x) { value = value * x.value % modulo; return *this; } inline ModInt& operator/=(const ModInt& rhs) { return *this*=rhs.inv(); } template ModInt operator+(const T& rhs)const { return ModInt(*this) += rhs; } template ModInt& operator+=(const T& rhs) { return operator+=(ModInt(rhs)); } template ModInt operator-(const T& rhs)const { return ModInt(*this) -= rhs; } template ModInt& operator-=(const T& rhs) { return operator-=(ModInt(rhs)); } template ModInt operator*(const T& rhs)const { return ModInt(*this) *= rhs; } template ModInt& operator*=(const T& rhs) { return operator*=(ModInt(rhs)); } template ModInt operator/(const T& rhs)const { return ModInt(*this) /= rhs; } template ModInt& operator/=(const T& rhs) { return operator/=(ModInt(rhs)); } }; std::istream& operator>>(std::istream& ist, ModInt& x) { lint a; ist >> a; x = a; return ist; } #line 3 "main.cpp" int n,m,k,a[45],b[45]; ModInt dp[45][45][45],fact[45],inv[45]; ModInt comb(int a,int b){ return fact[a]*inv[b]*inv[a-b]; } int main(){ std::cin>>n>>m>>k; REP(i,m)std::cin>>a[i]>>b[i]; ModInt ans=0,all=mypow(ModInt(k+1),n); REP(i,m)ans+=b[i]; ans*=all; fact[0]=1; rep(i,44)fact[i+1]=fact[i]*(i+1); inv[44]=ModInt(1)/fact[44]; for(int i=43;i>=0;i--)inv[i]=inv[i+1]*(i+1); REP(i,m){ std::vector vec={0,k+1}; std::unordered_map mp; REP(j,m){ if(b[j]>=b[i]){ vec.emplace_back(a[j]); mp[a[j]]++; } } int msize=vec.size()-2; std::sort(all(vec)); vec.erase(std::unique(all(vec)),vec.end()); rep(j,vec.size()){ rep(k,msize+1){ rep(l,n+1)dp[j][k][l]=0; } } dp[0][0][n]=1; rep(j,vec.size()-1){ rep(k,msize+1){ rep(l,n+1){ if(!dp[j][k][l])continue; ModInt memo=1; for(int o=std::max(0,k-msize+mp[vec[j]]);o<=l;o++){ if(a[i]<=vec[j]&&k-o+mp[vec[j]]<=0)break; dp[j+1][std::max(0,k-o+mp[vec[j]])][l-o]+=dp[j][k][l]*comb(l,o)*memo; memo*=vec[j+1]-vec[j]; } } } } ModInt sum=0; REP(j,msize)sum+=dp[vec.size()-1][j][0]; ans-=sum*b[i]; } std::cout<