#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) constexpr int inf = 1<<29; int const MOD = 1e9+7; typedef long long ll; constexpr int MATH_COMBINATION_MAX = 1010; /***********************************************************************************/ #define DEF_MAX_BOUND(assignment) enum { assignment }; #define MEMO_BEGIN(Identifier) \ namespace memorized { namespace Identifier { \ bool __computed = false; inline bool computed() {if(__computed) { return true; } else { __computed = true; return false; }} #define MEMO_END }} #define USE_MEMO(Identifier) using memorized::Identifier:: #define COMPUTED_RESULT(Identifier) if(memorized::Identifier::computed()) return #define USE_CONSTANT(Identifier) using memorized::Identifier:: /***********************************************************************************/ /* スターリング数 異なるN個をちょうどKグループに分けるときの方法の数 高々Kグループに分ける場合は、グループi(1<=i<=K)をN回選ぶ方法の数となり、これは単なる重複順列でK^Nとなる Verified: http://yukicoder.me/problems/663 */ namespace math { namespace combination { MEMO_BEGIN(stirling_number) DEF_MAX_BOUND(max_value = MATH_COMBINATION_MAX) ll dp[max_value][max_value]; MEMO_END int stirling_number(int N, int K) { USE_MEMO(stirling_number) dp; COMPUTED_RESULT(stirling_number) dp[N][K]; USE_CONSTANT(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]; dp[i][j] %= MOD; } } return dp[N][K]; } }} int N, M; vector g[222]; ll fact[MATH_COMBINATION_MAX]; ll dp[300][300]; int main() { cin >> N >> M; vector ws(N); rep(i, N) { cin >> ws[i]; } rep(i, M) { int a, b; cin >> a >> b; a--, b--; g[a].push_back(b); } 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])); } fact[0] = 1; rep(i, MATH_COMBINATION_MAX) 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; }