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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define ll              long long
#define pb              push_back
#define ppb             pop_back
#define endl            '\n'
#define mii             map<ll,ll>
#define pii             pair<ll,ll>
#define vi              vector<ll>
#define vs              vector<string>
#define all(a)          (a).begin(),(a).end()
#define F               first
#define S               second
#define sz(x)           ((ll)x.size())
#define hell            (1000000007)
#define inf             ((ll)5e18 + 5)
#define PI              ((double)3.14159265358979323844)
#define DECIMAL(n)      cout << fixed << setprecision(n);
#define rep(i,a,b)      for (ll i=a;i<b;i++)
#define repr(i,a,b)     for (ll i=a-1;i>=b;i--)
#define bitcount(a)     (ll)__builtin_popcount(a)
#define lbnd            lower_bound
#define ubnd            upper_bound
#define mp              make_pair
#define ios             ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define ordered_set     tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
#define trace(...)      __f(#__VA_ARGS__, __VA_ARGS__)

template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    std::cerr << name << " : " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');std::cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}

using namespace std;
using namespace __gnu_pbds;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//primes for hashing 937,991,1013,1409,1741

void solve() {
    ll n, k;
    cin>>n>>k;
    ll p[n], c[n];
    rep(i, 0, n) {
        cin>>p[i];
        p[i]--;
    }
    rep(i, 0, n) {
        cin>>c[i];
    }
    vi v;
    ll ans=-inf;
    bool vis[n]={0};
    ll tempk;
    rep(i, 0, n) {
        if (!vis[i]) {
            tempk=k;
            ll tempans=0;
            ll start=i;
            ll par=p[start];
            v.pb(c[start]);
            while(par!=start) {
                vis[par]=1;
                v.pb(c[par]);
                par=p[par];
            }
            ll totalCycle=0;
            for (auto y: v) {
                totalCycle+=y;
            }
            if (totalCycle>0) {
                tempans+=(k/sz(v)) * totalCycle;
                k%=sz(v);
            }
            else {
                if (k>=sz(v)) {
                    k=sz(v)-1;
                }
            }
            ll arr[sz(v)];
            rep(j, 0, sz(v)) {
                arr[j]=-inf;
            }
            rep(j, 0, sz(v)) {
                ll start1=j;
                ll prevSum=0;
                rep(x, 0, k) {
                    prevSum+=v[start1];
                    arr[j]=max(arr[j], prevSum);
                    start1=(start1+1)%sz(v);
                }
            }
            tempans+=*max_element(arr, arr+sz(v));
            ans=max(ans, tempans);
            v.clear();
            k=tempk;
        }
    }
    cout<<ans<<endl;
}

signed main() {
    ios
    ll test=1;
    //cin>>test;
    while (test--) solve();
    return 0;
}