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.

Examples

Input

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


Output

8


Input

2 3
2 1
10 -7


Output

13


Input

3 3
3 1 2
-1000 -2000 -3000


Output

-1000


Input

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


Output

29507023469
import java.util.*;
import java.io.*;
import java.math.*;

	
public class Main {
    static class Graph0n {
        private ArrayList<Node0n> dt = new ArrayList<>();
        Graph0n(int sz){for(int i=0; i<sz; i++){Node0n node1 = new Node0n();dt.add(node1);}}
        public void add(int vn, int val){       dt.get(vn).add(val);                    }
        public void add2(int vn, int val){      dt.get(vn).add(val);dt.get(val).add(vn);}
        public int get(int vn, int index){      return dt.get(vn).get(index);           }
        public ArrayList<Integer> get(int vn){  return dt.get(vn).getAll();             }
        public int size(){                      return dt.size();                       }
        public int sizeOf(int vn){              return dt.get(vn).size();               }
        public void clear(){    for(int i=0; i<dt.size(); i++){ dt.get(i).clear();  }   }
        public void clear(int i){    dt.get(i).clear();  }
        public static Graph0n make_tree(int vn, FastScanner sc){
        	Graph0n tree = new Graph0n(vn);
        	for(int i=1; i<vn; i++){
        	    int s1 = sc.nexI()-1;
        	    int g1 = sc.nexI()-1;
        	    tree.add2(s1,g1);
        	}
        	return tree;
        }
        private void add_Vertex(Node0n vnew){
            dt.add(vnew);
        }
    }
    static class Node0n {   //重みなし無向・有向グラフの頂点
        private ArrayList<Integer> next_vs = new ArrayList<>();
        public void add(int val){               next_vs.add(val);       }
        public int get(int ad){                 return next_vs.get(ad); }
        public ArrayList<Integer> getAll(){     return next_vs;         }
        public int size(){                      return next_vs.size();  }
        public void clear(){                    next_vs.clear();        }
        public void addAll(Node0n vnew){    this.next_vs.addAll(vnew.next_vs);   }
    }

    static class Edge {
        int from=-1, v2=-1;     long weight;
        public Edge(int vn, long w){
            this.v2 = vn;
            this.weight = w;
        }
        public Edge(int cm, int vn, long w){
            this.from = cm;
            this.v2 = vn;
            this.weight = w;
        }
    }
    static class Edge2 {
        int v2;     long cost1,cost2;
        public Edge2(int vn, long w1, long w2){
            this.v2 = vn;
            this.cost1 = w1;
            this.cost2 = w2;
        }
    }

    static class Comparator_Edge implements Comparator<Edge>{       //今は小さいのが前に出てくる
        public int compare(Edge a, Edge b){
            if(a.weight>b.weight) return 1;
            else if(a.weight<b.weight) return -1;
            else return a.v2-b.v2;
        }
    }
    
    static class Vector {
        int x,y;
        public Vector(int sx, int sy){
            this.x=sx;
            this.y=sy;
        }
    }
    
    
    //私が好きなアルゴリズム::累積和・UF木
    //PriorityQueueは拡張for文で出すとsortされてない順番で出てくるよ
    //longのbit演算は1L<<posに注意
    //long long
    //JOIはMLEが厳しい  shortというものがあるよ。あと、ArrayListはオートボクシングが遅いから、自作listが早いよ
	public static void main(String[] args) throws Exception {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nexI();
		long k = sc.nexL();
		int[] ps = new int[n];
		sc.aimin1(ps);
		long[] cs = new long[n];
		sc.al(cs);
		//小さいループがたくさん
		
		int[] szcycle = new int[n];
		long[][] scores = new long[n][n];
		fill(scores,-INFL);
		
		for(int i=0; i<n; i++){
		    int pos = i;
		    long ascore = 0L;
		    
		    for(int j=0; j<n; j++){
		        pos = ps[pos];
		        ascore += cs[pos];
		        scores[i][j] = ascore;
		        if(pos==i){
		            szcycle[i] = j+1;
		            break;
		        }
		    }
		}
		
        long ans = -INFL;
		for(int i=0; i<n; i++){
		    if(k<=szcycle[i]){
		        for(int j=0; j<k; j++){
		            ans = max(ans, scores[i][j]);
		        }   //一周もできない
		    }else{  //一周以上できる
	            ans = max(ans, maxExAd(scores[i], -1));
	            
		        if(scores[i][szcycle[i]-1] > 0){    //南洲もする価値あり
		            long rest = 0L;
    		        for(int j=0; j<(k%szcycle[i]); j++){
    		            rest = max(rest, scores[i][j]);
    		        }
    		        long ncy = k/(long)szcycle[i];
    		        rest += ncy*scores[i][szcycle[i]-1];
    		        
    		        ans = max(ans, rest);
    		        
    		        ans = max(ans, ((ncy-1)*scores[i][szcycle[i]-1])+ maxExAd(scores[i], -1));
		        }
		    }
		}
		out.println(ans);
		
		out.flush();
	}
	
	private static int INF = (int)1e8;
	private static long INFL = (long)1e17;
	private static long e97 = (long)1e9 + 7;
	
	private static void assertion(boolean b) { if(!b) throw new AssertionError(); }

	private static int abs(int a){  return (a>=0) ? a: -a;  }
	private static long abs(long a){    return (a>=0) ? a: -a;  }
	private static double abs(double a){    return (a>=0) ? a: -a;  }
	
	private static int min(int a, int b){   return (a>b) ? b : a;   }
	private static long min(long a, long b){    return (a>b) ? b : a;   }
	private static double min(double a, double b){    return (a>b) ? b : a;   }
	
	private static int max(int a, int b){   return (a>b) ? a : b;   }
	private static long max(long a, long b){    return (a>b) ? a : b;   }
	private static double max(double a, double b){    return (a>b) ? a : b;   }
	
	private static int minN(int... ins){
		int min = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] < min) min = ins[i];  }
		return min;
	}
	private static int maxN(int... ins){
		int max = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] > max) max = ins[i];  }
		return max;
	}
	private static long minN(long... ins){
		long min = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] < min) min = ins[i];  }
		return min;
	}
	private static long maxN(long... ins){
		long max = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] > max) max = ins[i];  }
		return max;
	}
	
	private static int minExAd(int[] dt, int ad){
	    int min=INF;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static long minExAd(long[] dt, int ad){
	    long min=INFL;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static int minExVal(int[] dt, int ex_val){
	    int min=INF;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static long minExVal(long[] dt, long ex_val){
	    long min=INFL;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static int maxExAd(int[] dt, int ad){
	    int max=-INF;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static long maxExAd(long[] dt, int ad){
	    long max=-INFL;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static double maxExAd(double[] dt, int ad){
	    double max=-INFL;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static int maxExVal(int[] dt, int ex_val){
	    int max=-INF;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static long maxExVal(long[] dt, long ex_val){
	    long max=-INFL;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] > max)) max = dt[i]; }
		return max;
	}

    private static int sumA(int[] dt){
        int sum =0;
        for(int e: dt){ sum += e; }
		return sum;
    }
    private static long sumA(long[] dt){
        long sum =0;
        for(long e: dt){ sum += e; }
		return sum;
    }
    private static int sumA(List<Integer> dt){
        int sum =0;
        for(long e: dt){ sum += e; }
		return sum;
    }
	
	private static double hypod(double a, double b){
	    return Math.sqrt(a*a+b*b);
	}
	
	private static long factorial(int n) {
		long ans=1;
		for(long i=n; i>0; i--){ ans*=i; }
		return ans;
	}
	
	private static long facP(int n, long p) {
		long ans=1;
		for(long i=n; i>0; i--){
		    ans*=i;
		    ans %= p;
		}
		return ans;
	}
	
	private static long lcm(long m, long n){
	    long ans = m/gcd(m,n);
	    ans *= n;
	    return ans;
	}
	
	private static long gcd(long m, long n) {
		if(m < n) return gcd(n, m);
		if(n == 0) return m;
		return gcd(n, m % n);
	}
	
	private static boolean is_prime(long a){
	    if(a==1) return false;
	    for(long i=2L; i<=Math.sqrt(a); i++){  if(a%i == 0) return false;  }
	    return true;
	}
	
    private static long modinv(long a, long p) {    //a|p, >1に注意
        long b = p, u = 1L, v = 0L;
        while (b>0) {
            long t = a / b;
            long pe = a%b;
            a=b;    b=pe;
            pe= u-t*v;
            u=v;    v=pe;
        }
        u %= p; 
        if (u < 0) u += p;
        return u;
    }
    
	private static int pow(int n, int k){
	    int ans=1;
	    for(int i=0; i<k; i++) ans *= n;
	    return ans;
	}
	private static long pow(long n, int k){
	    long ans=1;
	    for(int i=0; i<k; i++) ans *= n;
	    return ans;
	}
	
	private static int pow2(int in){            return in*in;   }
	private static long pow2(long in){          return in*in;   }
	private static double pow2(double in){      return in*in;   }
	
	private static int getDigit2(long num){
		long cf = 1;    int d=0;
		while(num > cf){   d++;    cf = (1L<<d);  }
		
		return d; //numは2^d以下
	}
	
	private static int getDigit10(long num){
		long cf = 1;    int d=0;
		while(num >= cf){   d++;    cf*=10;     }
		return d; //numはd桁の数で、10^dより小さい
	}
	
	private static boolean isINF(int in){
    	if(((long)in*20)>INF) return true;
    	else return false;
	}
	private static boolean isINFL(long in){
    	if((in*10000)>INFL) return true;
    	else return false;
	}
	
	private static long pow10E97(long ob, long soeji, long p){
	    if(ob==0) return 0;
	    if(soeji==0) return 1;
		if(soeji==2) return (ob*ob)%p;
		
		int d = getDigit2(soeji);
		long[] ob_pow_2pow = new long[d];
		
		ob_pow_2pow[0] = ob;
		for(int i=1; i<d; i++){ ob_pow_2pow[i] = (ob_pow_2pow[i-1]*ob_pow_2pow[i-1])%p;   }
		
		long ans=1;
		for(int i=d-1; i>=0; i--){
			if(soeji >= (long)(1<<i)){
				soeji -= (long)(1<<i);
				ans = (ans*ob_pow_2pow[i])%p;
			}
 		}
		return ans%p;
	}
	private static long nC2(long n){
		return ((n*(n-1))/2L);
	}
	private static int divceil(int numerator, int denominator){
	    return (numerator+denominator-1)/denominator;
	}
	private static long divceil(long numerator, long denominator){
	    return (numerator+denominator-1L)/denominator;
	}
	
	private static int iflag(int pos){               return (1<<pos);        }
	private static long flag(long pos){               return (1L<<pos);        }
	private static boolean isFlaged(int bit, int pos){
    	if((bit&(1<<pos)) > 0) return true;
    	else return false;
	}
	private static boolean isFlaged(long bit, int pos){
    	if((bit&(1L<<pos)) > 0) return true;
    	else return false;
	}
	private static int deflag(int bit, int pos){    return bit&~(1<<pos);   }
	private static int countFlaged(int bit){
	    int ans=0; 
	    for(int i=0; i<getDigit2(bit); i++){
	        if((bit&(1<<i)) > 0) ans++;
	    }
	    return ans;
	}
	private static int countFlaged(long bit){
	    int ans=0; 
	    for(long i=0; i<getDigit2(bit); i++){
	        if((bit&(1L<<i)) > 0) ans++;
	    }
	    return ans;
	}
	
	private static void show2(int bit){
    	for(int i=0; i<getDigit2(bit); i++){
        	if(isFlaged(bit,i)) System.out.print("O");
        	else System.out.print(".");
    	}
    	System.out.println();
	}
	
	public static int biSearch(int[] dt, int target){
		int left=0, right=dt.length-1;
		int mid=-1;
		while(left<=right){
			mid = (right+left)/2;
			if(dt[mid] == target) return mid;
			if(dt[mid] < target) left=mid+1;
			else right=mid-1;
		}
		return -1;
	}
	public static int biSearchMax(long[] dt, long target){
		int left=-1, right=dt.length;
		int mid=-1;
		
		while((right-left)>1){
			mid = left + (right-left)/2;
			if(dt[mid] <= target) left=mid;
			else right=mid;
		}
		return left;//target以下の最大のaddress
	}
	public static int biSearchMaxAL(ArrayList<Long> dt, long target){
		int left=-1, right=dt.size();
		int mid=-1;
		
		while((right-left)>1){
			mid = left + (right-left)/2;
			if(dt.get(mid) <= target) left=mid;
			else right=mid;
		}
		return left;//target以下の最大のaddress
	}
	
    private static int[] Xdir4 = {1,0,0,-1};
    private static int[] Ydir4 = {0,1,-1,0};
	    
	private	static int[] Xdir8 = {1,1,1,0,0,-1,-1,-1};
	private	static int[] Ydir8 = {1,0,-1,1,-1,1,0,-1};
	
	private static boolean is_in_area(int y, int x, int h, int w){
	    if(y<0) return false;
	    if(x<0) return false;
	    if(y>=h) return false;
	    if(x>=w) return false;
	    return true;
	}
	
	
	static void show2(boolean[][] dt, int lit_x, int lit_y){
		PrintWriter out = new PrintWriter(System.out);
		for(int j=0; j<dt.length; j++){
		    for(int i=0; i<dt[j].length; i++){
				if((i==lit_y) && (j==lit_x)) out.print("X");
				else if(dt[j][i]) out.print("O");
				else out.print(".");
			}
			out.println();
		}
		out.flush();
	}
	static void show2(int[][] dt, String cmnt){
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<dt.length; i++){
			for(int j=0; j<dt[i].length; j++){
				out.print(dt[i][j]+",");
			}
			out.println("<-"+cmnt+":"+i);
		}
		out.flush();
	}
	static void show2(long[][] dt, String cmnt){
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<dt.length; i++){
			for(int j=0; j<dt[i].length; j++){
				out.print(dt[i][j]+",");
			}
			out.println("<-"+cmnt+":"+i);
		}
		out.flush();
	}
	static void show2(ArrayDeque<Long> dt){		//上手くいかなかった時用
		long a=0;
		while(dt.size()>0){
			a=dt.removeFirst();
			System.out.print(a);
		}
		System.out.println("\n");
	}
	static void show2(List dt){		//上手くいかなかった時用
	   	for(int i=0; i<dt.size(); i++){
			System.out.print(dt.get(i)+",");
		}
		System.out.println("\n");
	}
	
	
	private static void prtlnas(int[] as){
		PrintWriter out = new PrintWriter(System.out);
	    for(int i=0; i<as.length; i++){
	        out.println(as[i]);
	    }
	    out.flush();
	}
	private static void prtlnas(long[] as){
		PrintWriter out = new PrintWriter(System.out);
	    for(int i=0; i<as.length; i++){
	        out.println(as[i]);
	    }
	    out.flush();
	}
	private static void prtspas(int[] as){
		PrintWriter out = new PrintWriter(System.out);
		out.print(as[0]);
	    for(int i=1; i<as.length; i++){
	        out.print(" "+as[i]);
	    }
	    out.println();
	    out.flush();
	}
	private static void prtspas(long[] as){
		PrintWriter out = new PrintWriter(System.out);
		out.print(as[0]);
	    for(int i=1; i<as.length; i++){
	        out.print(" "+as[i]);
	    }
	    out.println();
	    out.flush();
	}
	private static void prtspas(List as){
		PrintWriter out = new PrintWriter(System.out);
		out.print(as.get(0));
	    for(int i=1; i<as.size(); i++){
	        out.print(" "+as.get(i));
	    }
	    out.println();
	    out.flush();
	}
	
	
    private static void fill(boolean[] ob, boolean res){    for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
    private static void fill(int[] ob, int res){            for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(long[] ob, long res){          for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(char[] ob, char res){          for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(double[] ob, double res){      for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(boolean[][] ob,boolean res){for(int i=0;i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(int[][] ob, int res){      for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(long[][] ob, long res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(char[][] ob, char res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(double[][] ob, double res){for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(int[][][] ob,int res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
	private static void fill(long[][][] ob,long res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
	
    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 nexL() {
    		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) || b == ':'){
    				return minus ? -n : n;
    			}else{
    				throw new NumberFormatException();
    			}
    			b = readByte();
    		}
    	}
    	public int nexI() {
    		long nl = nexL();
    		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
    		return (int) nl;
    	}
    	public double nexD() { return Double.parseDouble(next());}
    	
    	public void al(long[] array){
    	   	for(int i=0; i<array.length; i++){
    	   	    array[i] = nexL();
    	   	}
    	   	return;
    	}
    	public void ai(int[] array){
    	   	for(int i=0; i<array.length; i++){
    	   	    array[i] = nexI();
    	   	}
    	   	return;
    	}
    	public void aimin1(int[] array){
    	   	for(int i=0; i<array.length; i++){
    	   	    array[i] = nexI()-1;
    	   	}
    	   	return;
    	}
    	public void aD(double[] array){
    	   	for(int i=0; i<array.length; i++){
    	   	    array[i] = nexD();
    	   	}
    	   	return;
    	}
    	public void ai2(int[] as, int[] bs){
    	   	for(int i=0; i<as.length; i++){
    	   	    as[i] = nexI();
    	   	    bs[i] = nexI();
    	   	}
    	   	return;
    	}
    	public void al2(long[] as, long[] bs){
    	   	for(int i=0; i<as.length; i++){
    	   	    as[i] = nexL();
    	   	    bs[i] = nexL();
    	   	}
    	   	return;
    	}
    	public void ai3(int[] as, int[] bs, int[] cs){
    	   	for(int i=0; i<as.length; i++){
    	   	    as[i] = nexI();
    	   	    bs[i] = nexI();
    	   	    cs[i] = nexI();
    	   	}
    	   	return;
    	}
    	public void ad2i(int[][] as){
    	    for(int i=0; i<as.length; i++){
    	        for(int j=0; j<as[0].length; j++){
    	            as[i][j] = nexI();
    	        }
    	    }
    	    return;
    	}
    	public void ain(int[]... as){
    	    for(int i=0; i<as[0].length; i++){
    	        for(int j=0; j<as.length; j++){
    	            as[j][i] = nexI();
    	        }
    	    }
    	}
    	public void aln(long[]... as){
    	    for(int i=0; i<as[0].length; i++){
    	        for(int j=0; j<as.length; j++){
    	            as[j][i] = nexL();
    	        }
    	    }
    	}
    }
}