#pragma GCC optimize("Ofast") #include using namespace std; using ll = long long int ; using ld = long double ; using P = pair; using Graph= vector>; struct edge{ll to ; ll cost ;} ; using graph =vector> ; #define rep(i,n) for (ll i=0; i < (n); ++i) #define rep2(i,n,m) for(ll i=n;i<=m;i++) #define rep3(i,n,m) for(ll i=n;i>=m;i--) #define pb push_back #define eb emplace_back #define ppb pop_back #define mpa make_pair #define fi first #define se second #define set20 cout<= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, const mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} //昆布 struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { assert(n < mod); //任意modではここ消すcombmain内に fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } mint p(int n,int k){ return fact[n]*ifact[n-k] ; //kは個数 } } c(6005) ; mint modpow(ll a,ll b){ if(b==0) return 1 ; mint c= modpow(a,b/2) ; if(b%2==1) return c*c*a ; else return c*c ; } mint mmodpow(mint a,ll b){ if(b==0) return 1ll ; mint c=mmodpow(a,(b/2)) ; if(b%2==1) return c*c*a ; else return c*c ; } mint komb(ll n,ll m){ mint x=1 ;mint y=1 ; rep(i,m){ x*= n-i ; y*= i+1 ; } return x/y ; } map factor(ll n){ //素因数とオーダーをマップで管理 map ord ; for(ll i=2;i*i<=n;i++){ if(n%i==0){ int res=0; while(n%i==0){ n/=i; res++; } ord[i]=res; } } if(n!=1) ord[n]++; return ord ; } struct UnionFind { vector d; UnionFind(int n=0): d(n,-1) {} int find(int x) { if (d[x] < 0) return x; return d[x] = find(d[x]); } bool unite(int x, int y) { x = find(x); y = find(y); if (x == y) return false; if (d[x] > d[y]) swap(x,y); d[x] += d[y]; d[y] = x; return true; } bool same(int x, int y) { return find(x) == find(y);} int size(int x) { return -d[find(x)];} }; // sum(x) x以下の和 // sum(a,b) a以上b以下の和 template struct BIT { int n; vector d; BIT(int n=0):n(n),d(n+1) {} void add(int i, T x=1) { //x=1ならsumは個数のカウント for (i++; i <= n; i += i&-i) { d[i] += x; } } T sum(int i) { T x = 0; for (i++; i; i -= i&-i) { x += d[i]; } return x; } T sum(int i,int j) { if(i>0) return sum(j)-sum(i-1); else return sum(j); } }; int main(){ ios::sync_with_stdio(false) ; cin.tie(nullptr) ; ll n,m; cin>>n>>m; vector A(n); rep(i,n) cin>>A[i]; rep(i,n) A[i]--; vector x; vector seen(n); rep(i,n){ ll now=i; ll cnt=0ll; if(!seen[i]){ while(!seen[now]){ seen[now]=true; cnt++; now=A[now]; } x.pb(cnt); } } mint sum=0ll; mint dp[5005][5005]; rep(i,5005){ rep(j,5005){ if(j==0) dp[i][j]=1ll; else dp[i][j]=dp[i][j-1]*i; } } rep2(i,0,m-1){ mint ans=1; ll k=m-i; /* for(auto u:x){ if(u%2) ans*=((dp[k-1][u-1]-1ll)/k)*(k-1)*(k); //if(u%2) ans*=((modpow(k-1,u-1)-1ll)/k)*(k-1)*k; else ans*=((dp[k-1][u-1]+1ll)/k)*(k-1)*(k); //else ans*=((modpow(k-1,u-1)+1ll)/k)*(k-1)*k; } */ if(i%2) sum-=ans*c(m,i); else sum+=ans*c(m,i); } rep2(i,1,m) sum/=i; cout<