import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Scanner;
import java.util.function.BinaryOperator;

public class Main implements Runnable {

	public static void main(String[] args) throws IOException {
		new Thread(null, new Main(), "", Runtime.getRuntime().maxMemory()).start();
	}
	
	
	long inv(long a) {
		return pow(a,p-2);
	}
	
	long ADD(long a,long b) {
		return a+b>=p?a+b-p:a+b;
	}
	
	long SUB(long a,long b) {
		return ADD(a,p-b);
	}
	
	long[] mul(long[] a, long[] b) {
		long[] c=new long[a.length+b.length-1];
		for (int i=0;i<a.length;++i) {
			for (int j=0;j<b.length;++j) {
				c[i+j]+=a[i]*b[j];
				c[i+j]%=p;
			}
		}
		return c;
	}
	
	
	long[] inv(long[] a) {
		int n=a.length;
		long[] G= {inv(a[0])};
		for (int len=1;len<n;len*=2) {
			long[] prd=mul(mul(G,G),Arrays.copyOf(a, 2*len));
			G=Arrays.copyOf(G, 2*len);
			for (int i=0;i<2*len;++i) {
				G[i]=(2*G[i]+p-prd[i])%p;
			}
		}
		return G;
	}
	
	long[] differentiate(long[] a) {
		long[] ret=new long[a.length];
		for (int i=0;i+1<ret.length;++i) ret[i]=(i+1)*a[i+1]%p;
		return ret;
	}
	
	long[] integrate(long[] a) {
		long[] ret=new long[a.length];
		for (int i=0;i+1<ret.length;++i) ret[i+1]=inv(i+1)*a[i]%p;
		return ret;
	}
	
	long[] log(long[] a) {
		return integrate(mul(differentiate(a),inv(a)));
	}
	
	long[] exp(long[] a) {
		int n=a.length;
		long[] G= {1};
		for (int len=1;len<n;len*=2) {
			long[] log=log(Arrays.copyOf(G, 2*len));
			for (int i=0;i<Math.min(n,2*len);++i) log[i]=(p-log[i]+a[i])%p;
			log[0]=ADD(log[0],1);
			G=Arrays.copyOf(mul(G,log),2*len);
		}
		return G;
	}
	
	class UnionFind {
		int[] parent;
		public UnionFind(int n) {
			parent=new int[n];
			Arrays.fill(parent, -1);
		}
		int root(int x) {
			return parent[x]<0?x:(parent[x]=root(parent[x]));
		}
		boolean isroot(int x) {
			return parent[x]<0;
		}
		boolean equiv(int x, int y) {
			return root(x)==root(y);
		}
		void union(int x, int y) {
			x=root(x);
			y=root(y);
			if (x==y) return;
			parent[y]+=parent[x];
			parent[x]=y;
		}
		int sz(int x) {
			return -parent[root(x)];
		}
	}
	
	final long p=(long)1e9+7;
	
	long pow(long a, long n) {
		if (n==0) return 1;
		return pow(a*a%p,n/2)*(n%2==1?a:1)%p;
	}
	
	long gcd(long a, long b) {
		if (a==0) return b;
		return gcd(b%a, a);
	}
	
	int MAX=10000;
	long[] fac=new long[MAX];
	long[] inv=new long[MAX];
	long[] ifac=new long[MAX];
	{
		Arrays.fill(fac, 1);
		Arrays.fill(ifac, 1);
		Arrays.fill(inv, 1);
		for (int i=2;i<MAX;++i) {
			fac[i]=fac[i-1]*i%p;
			inv[i]=p-(p/i)*inv[(int)(p%i)]%p;
			ifac[i]=inv[i]*ifac[i-1]%p;
		}
	}
	public void run() {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int N=sc.nextInt();
		int M=sc.nextInt();
		int[] A=new int[N];
		for (int i=0;i<N;++i) A[i]=sc.nextInt()-1;
		UnionFind uf=new UnionFind(N);
		for (int i=0;i<N;++i) uf.union(i, A[i]);
		int[] cnt=new int[N+1];
		for (int i=0;i<N;++i) {
			if (uf.isroot(i)) cnt[uf.sz(i)]++;
		}
		long ans=1;
		for (int len=1;len<=N;++len) {
			long[] f=new long[cnt[len]+1];
			for (int n=1;n<=cnt[len];++n) {
				if (M%n!=0) continue;
				if (gcd(M/n,len)!=1) continue;
				f[n]=pow(len, n-1)*fac[n-1]%p*ifac[n]%p;
			}
			f=exp(f);
			int t=cnt[len];
			ans=ans*f[t]%p*fac[t]%p;
		}
		System.out.println(ans);
	}

	
	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		return (int) nextLong();
	}
}