Problem:
Score : 400 points

Problem Statement

Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.

Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

2 \leq N \leq 5000

1 \leq K \leq 10^9

1 \leq P_i \leq N

P_i \neq i

P_1, P_2, \cdots, P_N are all different.

-10^9 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N

Output

Print the maximum possible score at the end of the game.

Sample Input 1

5 2
2 4 5 1 3
3 4 -10 -8 8

Sample Output 1

8

When we start at some square of our choice and make at most two moves, we have the following options:

If we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.

If we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.

If we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.

If we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.

If we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.

The maximum score achieved is 8.

Sample Input 2

2 3
2 1
10 -7

Sample Output 2

13

Sample Input 3

3 3
3 1 2
-1000 -2000 -3000

Sample Output 3

-1000

We have to make at least one move.

Sample Input 4

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719

Sample Output 4

29507023469

The absolute value of the answer may be enormous.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.*;

import java.io.*;
import java.util.*;
import java.util.PriorityQueue;

public class Main {
	public static long gcd(long n, long m){ if(m > n) return gcd(m,n); if(m == 0) return n; return gcd(m, n%m);}
	public static long lcm(long m, long n){ return (m/gcd(m,n))*n;}
	static int mod = 998244353;
	static int INF = Integer.MAX_VALUE;
	static int[] dx = {0,0,1,-1};
	static int[] dy = {1,-1,0,0};
	static int[] dx8 = {0,0,1,-1,1,1,-1,-1};
	static int[] dy8 = {1,-1,0,0,1,-1,-1,1};
	public static void main(String[] args){
		FastScanner scanner = new FastScanner();
		int n = scanner.nextInt();
		int k = scanner.nextInt();
		int[] p = new int[n];
		int[] c = new int[n];
		for(int i = 0; i < n; i++){
			p[i] = scanner.nextInt()-1;
		}
		for(int i = 0; i < n; i++){
			c[i] = scanner.nextInt();
		}
		long[][] cost = new long[n][n];
		boolean[] f = new boolean[n]; //一周回って和が負になる時True
		UnionFind uf = new UnionFind(n);
		for(int i = 0; i < n; i++){
			int now = i;
			int start = i;
			long sum = 0;
			while(true){
				now = p[now];
				sum += c[now];
				uf.unite(now,p[now]);
				cost[start][now] = sum;
				if(now == start) break;
			}
			if(sum < 0) f[i] = true;
		}
		long ans = -INF;
		for(int i = 0; i < n; i++){
			if(f[i]){
				int num = uf.size(i);
				int now = i;
				long s = 0;
				if(num >= k){
					while(num > 0){
						now = p[now];
						s += c[now];
						num--;
						ans = Math.max(ans,s);
					}
				}else if(num < k){
					while(num > 0){
						now = p[now];
						s += c[now];
						num--;
						ans = Math.max(ans,s);
					}
				}
			}else if(!f[i]){
				long cycle = k/uf.size(i);
				int num = k % uf.size(i);
				long s = cost[i][i] * cycle;
				int now = i;
				while(num > 0){
					now = p[now];
					s += c[now];
					num--;
					ans = Math.max(ans,s);
				}
			}
		}
		System.out.println(ans);
	}

	  static class UnionFind {
	    int[] parent;
	    public UnionFind(int size) {
	      parent = new int[size];
	      Arrays.fill(parent, -1);
	    }
	    public boolean unite(int x, int y) {
	      x = root(x);
	      y = root(y);
	      if (x != y) {
	        if (parent[y] < parent[x]) {
	          int tmp = y;
	          y = x;
	          x = tmp;
	        }
	        parent[x] += parent[y];
	        parent[y] = x;
	        return true;
	      }
	      return false;
	    }
	    public boolean same(int x, int y) {
	      return root(x) == root(y);
	    }
	    public int root(int x) {
	      return parent[x] < 0 ? x : (parent[x] = root(parent[x]));
	    }
	    public int size(int x) {
	      return -parent[root(x)];
	    }
	  }
	public static final int lowerBound(final int[] arr, final int value) {
		 int low = 0;
		 int high = arr.length;
		 int mid;
		 while (low < high){
				 mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
				 if (arr[mid] < value) {
					 low = mid + 1;
				 } else {
					 high = mid;
				 }
		 }
		 return low;
	 }
	public static int upperBound(int[] array, int value) {
			 int low = 0;
			 int high = array.length;
			 int mid;
			 while( low < high ) {
					 mid = ((high - low) >>> 1) + low; // (high + low) / 2
					 if( array[mid] <= value ) {
							 low = mid + 1;
					 } else {
							 high = mid;
					 }
			 }
			 return low;
	 }
	public static boolean isPrime(int n){
		if(n == 1) return false;
		if(n == 2 || n == 3) return true;
		for(int i = 2; i <= Math.sqrt(n); i++){
			if(n % i == 0) return false;
		}
		return true;
	}
	public static char i2c(int i){
		if(0 <= i && i < 26){
			return (char)(i + 'a');
		}else{
			return (char)(i + 'A' - 26);
		}
	}
	static class Point{
		int x; int y;
		Point(int x, int y){
			this.x = x;
			this.y = y;
		}
	}
	static class Edge{
		int to;
		Edge(int to){
			this.to = to;
		}
	}
	static class Edge2 implements Comparable<Edge2>{
		int from;
		int to;
		int cost;
		Edge2(int from, int to, int cost){
			this.from = from;
			this.to = to;
			this.cost = cost;
		}
		public int compareTo(Edge2 e){
			return cost-e.cost;
		}
	}

	static class RMQ {
		private int size_, dat[];
		private int query_(int a, int b, int k, int l, int r) {
			if(r <= a || b <= l) return 2147483647;
			if(a <= l && r <= b) return dat[k];
			int lc = query_(a, b, 2 * k, l, (l + r) / 2);
			int rc = query_(a, b, 2 * k + 1, (l + r) / 2, r);
			return Math.min(lc, rc);
		}
		RMQ(int s) {
			for(size_ = 1; size_ < s;) size_ *= 2;
			dat = new int[size_ * 2];
			for(int i = 0; i < size_ * 2; i++) dat[i] = 2147483647;
		}
		public void update(int pos, int x) {
			pos += size_; dat[pos] = x;
			while(pos > 1) {
				pos /= 2;
				dat[pos] = Math.min(dat[2 * pos], dat[2 * pos + 1]);
			}
		}
		public int query(int l, int r) {
			return query_(l, r, 1, 0, size_);
		}
	}
	static int size = 2100000;
	static long[] fac = new long[size];
	static long[] finv = new long[size];
	static long[] inv = new long[size];
	//繰り返し二乗法
	public static long pow(long x, long n){
		long ans = 1;
		while(n > 0){
			if((n & 1) == 1){
				ans = ans * x;
				ans %= mod;
			}
			x = x * x % mod;
			n >>= 1;
		}
		return ans;
	}
	public static long div(long x, long y){
		return (x*pow(y, mod-2))%mod;
	}
	//fac, inv, finvテーブルの初期化、これ使う場合はinitComb()で初期化必要
	public static  void initComb(){
		fac[0] = finv[0] = inv[0] = fac[1] = finv[1] = inv[1] = 1;
		for (int i = 2; i < size; ++i) {
			fac[i] = fac[i - 1] * i % mod;
			inv[i] = mod - (mod / i) * inv[(int) (mod % i)] % mod;
			finv[i] = finv[i - 1] * inv[i] % mod;
		}
	}
	//nCk % mod
	public static long comb(int n, int k){
		return fac[n] * finv[k] % mod * finv[n - k] % mod;
	}
	//n! % mod
	public static long fact(int n){
		return fac[n];
	}
	//(n!)^-1 with % mod
	public static long finv(int n){
		return finv[n];
	}
	private static 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;}
		public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; 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() {
				long nl = nextLong();
				if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
				return (int) nl;
		}
		public double nextDouble() { return Double.parseDouble(next());}
	}
}