#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define REP(i,a,b) for(int i=a;i<(int)b;i++) #define rep(i,n) REP(i,0,n) #define all(c) (c).begin(), (c).end() #define zero(a) memset(a, 0, sizeof a) #define minus(a) memset(a, -1, sizeof a) #define minimize(a, x) a = std::min(a, x) #define maximize(a, x) a = std::max(a, x) #define int long long constexpr int inf = 1<<29; int const MOD = 1e9+7; typedef long long ll; namespace math { namespace combination { // experimental #define COMBINATION_MAX 1010 namespace memorized { namespace stirling_number { enum { max_value = COMBINATION_MAX }; bool __computed = false; inline bool computed() {if(__computed) { return true; } else { __computed = true; return false; }} ll dp[max_value][max_value]; }} ll stirling_number(int N, int K) { using memorized::stirling_number::dp; if(memorized::stirling_number::computed()) { return dp[N][K]; } // Make stirling numbers using memorized::stirling_number::max_value; REP(i, 1, max_value) { // undefined when i = 0 dp[i][1] = dp[i][i] = 1; REP(j, 2, i) { dp[i][j] = dp[i-1][j-1] + j * dp[i-1][j]; } } return dp[N][K]; } }} signed main() { int N, M; cin >> N >> M; vector ws(N); rep(i, N) { cin >> ws[i]; } vector g[222]; rep(i, M) { int a, b; cin >> a >> b; a--, b--; g[a].push_back(b); } ll dp[N+1][N+1]; zero(dp); rep(i, N) { dp[i][i] = ws[i]; rep(j, g[i].size()) { int tar = g[i][j]; dp[i][tar] = min(dp[i][i], ws[tar]); } } rep(k, N) rep(i, N) rep(j, N) { maximize(dp[i][j], min(dp[i][k], dp[k][j])); } ll fact[1010]; fact[0] = 1; rep(i, 1000) fact[i+1] = fact[i] * (i+1) % MOD; // 異なるN個を異なるK個に振り分ける方法の数(全射の数) := S(N, K) * K! using math::combination::stirling_number; ll ans = 0; rep(i, N) rep(j, N) { if(dp[i][j] < ws[j]) { continue; } ans += stirling_number(ws[i], ws[j]) * fact[ws[j]] % MOD; ans %= MOD; } cout << ans << endl; return 0; }