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 (Clang 10.0.0) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <limits.h>
#include <ctype.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>
#include <math.h>

#define N_MAX (100)
#define P_MAX (100)
#define DP_ARRAY_SIZE (N_MAX * P_MAX / 32 + 1)

#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define ABS(a) ((a) < 0 ? -(a) : (a))
#define ABSS(a, b) ((a) > (b) ? (a) - (b) : (b) - (a))
#define SWAP(type, a, b) { const type tmp = a; a = b; b = tmp; }

int compare_sz_asc(const void* a, const void* b) {
    return *((size_t*)a) < *((size_t*)b) ? -1 : 1;
}

int compare_sz_desc(const void* a, const void* b) {
    return *((size_t*)a) > * ((size_t*)b) ? -1 : 1;
}

int compare_i64_asc(const void* a, const void* b) {
    return *((int64_t*)a) < *((int64_t*)b) ? -1 : 1;
}

int compare_i64_desc(const void* a, const void* b) {
    return *((int64_t*)a) > * ((int64_t*)b) ? -1 : 1;
}

int compare_u64_asc(const void* a, const void* b) {
    return *((uint64_t*)a) < *((uint64_t*)b) ? -1 : 1;
}

int compare_u64_desc(const void* a, const void* b) {
    return *((uint64_t*)a) > * ((uint64_t*)b) ? -1 : 1;
}

int compare_c_asc(const void* a, const void* b) {
    return *((char*)a) < *((char*)b) ? -1 : 1;
}

int compare_c_desc(const void* a, const void* b) {
    return *((char*)a) > * ((char*)b) ? -1 : 1;
}

int compare_dp_asc(const void* a, const void* b) {
    return *((double*)a) < *((double*)b) ? -1 : 1;
}

static uint64_t modinvU64(const uint64_t a, const uint64_t m) {
    int64_t aa = (int64_t)a;
    const int64_t mm = (int64_t)m;
    int64_t b = mm;
    int64_t u = 1;
    int64_t v = 0;

    while (b != 0) {
        const int64_t t = aa / b;

        aa -= t * b;
        SWAP(uint64_t, aa, b);
        u -= t * v;
        SWAP(uint64_t, u, v);
    }

    u %= mm;
    if (u < 0) {
        u += m;
    }

    return (uint64_t)u;
}

static size_t powSz(const size_t base, const size_t exp) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base;
    }

    if (exp % 2 == 0) {
        return powSz(base * base, exp / 2);
    }
    else {
        return base * powSz(base, exp - 1);
    }
}

static uint64_t powU64(const uint64_t base, const uint64_t exp) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base;
    }

    if (exp % 2 == 0) {
        return powU64(base * base, exp / 2);
    }
    else {
        return base * powU64(base, exp - 1);
    }
}

static uint64_t powU64WMod(const uint64_t base, const uint64_t exp, const uint64_t m) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base % m;
    }

    if (exp % 2 == 0) {
        return powU64WMod(base * base % m, exp / 2, m);
    }
    else {
        return base * powU64WMod(base, exp - 1, m) % m;
    }
}

static size_t combSz(const size_t n, const size_t r) {
    size_t result = 1;

    for (size_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t combU64(const uint64_t n, const uint64_t r) {
    uint64_t result = 1;

    for (uint64_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t combU64WMod(const uint64_t n, const uint64_t r, const uint64_t m) {
    uint64_t result = 1;
    uint64_t inv = 1;

    for (uint64_t i = 0; i < r; i++) {
        result = result * (n - i) % m;
        inv = inv * (i + 1) % m;
    }

    return result * modinvU64(inv, m) % m;
}

static uint64_t permU64(const uint64_t n) {
    uint64_t result = 1;

    for (uint64_t v = 2; v <= n; v++) {
        result *= v;
    }

    return result;
}

static uint64_t permU64WMod(const uint64_t n, const uint64_t m) {
    uint64_t result = 1;

    for (uint64_t v = 2; v <= n; v++) {
        result *= v;
        result %= m;
    }

    return result;
}

static size_t gcdZu(size_t m, size_t n) {
    size_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

static uint64_t gcdU64(uint64_t m, uint64_t n)
{
    uint64_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

static uint64_t popcntU64(uint64_t val) {
    uint64_t cnt = 0;

    while (val != 0) {
        if ((val & UINT64_C(0x1)) != 0) {
            cnt++;
        }

        val >>= UINT64_C(0x1);
    }

    return cnt;
}

typedef struct {
    uint64_t val;
}BHeap_Val;

#define BHEAP_VAL_TYPE BHeap_Val

#define BHEAP_INVALID_NODE ((size_t)100000000)

typedef struct {
    BHEAP_VAL_TYPE val;
} BHeap_Node;


struct _BHeap_Ctx {
    size_t size;
    int (*compare)(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node);
    void(*notifyNodeChange)(const struct _BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList);
    BHeap_Node* node;
};

typedef struct _BHeap_Ctx BHeap_Ctx;

static void bHeap_Init(BHeap_Ctx* const ctx, int(*compare)(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node), void(*notifyNodeChange)(const BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList), BHeap_Node* const nodes) {
    ctx->size = 0;
    ctx->compare = compare;
    ctx->notifyNodeChange = notifyNodeChange;
    ctx->node = nodes;
}

static void bHeap_Swap(BHeap_Ctx* const ctx, const size_t node0, const size_t node1) {
    const BHEAP_VAL_TYPE tmp = ctx->node[node0].val;
    ctx->node[node0].val = ctx->node[node1].val;
    ctx->node[node1].val = tmp;

    if (ctx->notifyNodeChange != NULL) {
        const size_t nodeList[2] = { node0,node1 };
        ctx->notifyNodeChange(ctx, 2, nodeList);
    }
}

static void bHeap_UpHeap(BHeap_Ctx* const ctx, const size_t nodeIdx) {
    if (nodeIdx == 0) {
        return;
    }

    const size_t parentIdx = (nodeIdx + 1) / 2 - 1;

    const int compareResult = ctx->compare(&(ctx->node[parentIdx].val), &(ctx->node[nodeIdx].val));

    if (0 < compareResult) {
        bHeap_Swap(ctx, nodeIdx, parentIdx);

        if (parentIdx != 0) {
            bHeap_UpHeap(ctx, parentIdx);
        }
    }
}

static void bHeap_DownHeap(BHeap_Ctx* const ctx, const size_t nodeIdx) {
    if (ctx->size - 1 <= nodeIdx) {
        return;
    }

    const size_t leftIdx = 2 * (nodeIdx + 1) - 1;

    if (leftIdx < ctx->size) {
        const int leftResult = ctx->compare(&(ctx->node[nodeIdx].val), &(ctx->node[leftIdx].val));

        size_t swapTarget = leftResult < 0 ? BHEAP_INVALID_NODE : leftIdx;

        const size_t rightIdx = leftIdx + 1;

        if (rightIdx < ctx->size) {
            const int rightResult = ctx->compare(&(ctx->node[nodeIdx].val), &(ctx->node[rightIdx].val));

            if (swapTarget == BHEAP_INVALID_NODE) {
                if (0 < rightResult) {
                    swapTarget = rightIdx;
                }
            }
            else {
                if (0 < rightResult) {
                    const int rightLeftResult = ctx->compare(&(ctx->node[leftIdx].val), &(ctx->node[rightIdx].val));

                    if (0 < rightLeftResult) {
                        swapTarget = rightIdx;
                    }
                }
            }
        }

        if (swapTarget != BHEAP_INVALID_NODE) {
            bHeap_Swap(ctx, nodeIdx, swapTarget);

            bHeap_DownHeap(ctx, swapTarget);
        }
    }
}

static void bHeap_Add(BHeap_Ctx* const ctx, const BHEAP_VAL_TYPE val) {
    ctx->node[ctx->size].val = val;

    ctx->size++;

    if (ctx->notifyNodeChange != NULL) {
        const size_t node = ctx->size - 1;
        ctx->notifyNodeChange(ctx, 1, &node);
    }

    bHeap_UpHeap(ctx, ctx->size - 1);
}

static void bHeap_RemoveTop(BHeap_Ctx* const ctx) {
    if (ctx->size == 0) {
        return;
    }

    if (ctx->size == 1) {
        ctx->size--;
        return;
    }

    ctx->node[0].val = ctx->node[ctx->size - 1].val;

    if (ctx->notifyNodeChange != NULL) {
        const size_t node = 0;
        ctx->notifyNodeChange(ctx, 1, &node);
    }

    ctx->size--;

    bHeap_DownHeap(ctx, 0);
}

static void bHeap_RemoveNode(BHeap_Ctx* const ctx, const size_t node) {
    if (node == ctx->size - 1) {
        ctx->size--;
    }
    else {
        ctx->node[node].val = ctx->node[ctx->size - 1].val;

        ctx->size--;

        if (ctx->notifyNodeChange != NULL) {
            ctx->notifyNodeChange(ctx, 1, &node);
        }

        bHeap_DownHeap(ctx, node);
        bHeap_UpHeap(ctx, node);
    }
}

static BHEAP_VAL_TYPE* bHeap_GetTopVal(const BHeap_Ctx* const ctx) {
    return ctx->size == 0 ? NULL : &(ctx->node[0].val);
}

typedef struct {
    uint64_t cnt;
    size_t* child;
    size_t numChild;
    size_t maxNumChild;
} Tree_Node;

#define TREE_INIT_ALLOC (128)

static Tree_Node tree_Node[200000];

static void tree_Init(const uint64_t N) {
    for (uint64_t i = 0; i < N; i++) {
        tree_Node[i].cnt = 0;
        tree_Node[i].numChild = 0;
        tree_Node[i].child = malloc(sizeof(size_t) * TREE_INIT_ALLOC);
        tree_Node[i].maxNumChild = TREE_INIT_ALLOC;
    }
}

static void tree_AddChild(const size_t parent, const size_t child) {
    if (tree_Node[parent].maxNumChild <= tree_Node[parent].numChild) {
        tree_Node[parent].child = realloc(tree_Node[parent].child, sizeof(size_t) * tree_Node[parent].maxNumChild * 2);
        tree_Node[parent].maxNumChild *= 2;
    }

    tree_Node[parent].child[tree_Node[parent].numChild] = child;
    tree_Node[parent].numChild++;
}

static BHeap_Node BN_Asc[200000];
static BHeap_Node BN_Desc[200000];

static int _bHeap_Compare_Asc(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node) {
    return parent->val <= node->val ? -1 : 1;
}

static int _bHeap_Compare_Desc(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node) {
    return parent->val >= node->val ? -1 : 1;
}

static size_t PBHeap_Asc_Idx[200000];
static size_t PBHeap_Desc_Idx[200000];

static void _bHeap_NotifyNodeChange_Asc(const BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList) {
    for (size_t i = 0; i < nodeListSize; i++) {
        PBHeap_Asc_Idx[ctx->node[nodeList[i]].val.val] = nodeList[i];
    }
}

static void _bHeap_NotifyNodeChange_Desc(const BHeap_Ctx* const ctx, const size_t nodeListSize, const size_t* const nodeList) {
    for (size_t i = 0; i < nodeListSize; i++) {
        PBHeap_Desc_Idx[ctx->node[nodeList[i]].val.val] = nodeList[i];
    }
}

#define UF_ROOT ((size_t)10000000)

typedef struct {
    size_t parent;
    uint64_t w;
    uint64_t v;
    uint64_t wSum;
    uint64_t vSum;
} UF_Node;

static UF_Node uf_Node[101];

static size_t uf_GetRoot(const size_t idx) {
    if (uf_Node[idx].parent == UF_ROOT) {
        return idx;
    }

    const size_t root = uf_GetRoot(uf_Node[idx].parent);

    uf_Node[idx].parent = root;

    return root;
}

static void uf_Merge(const size_t a, const size_t b) {
    const size_t aRoot = uf_GetRoot(a);
    const size_t bRoot = uf_GetRoot(b);

    if (aRoot != bRoot) {
        uf_Node[aRoot].parent = bRoot;

        uf_Node[bRoot].wSum += uf_Node[aRoot].wSum;
        uf_Node[bRoot].vSum += uf_Node[aRoot].vSum;
    }
}

static void sha1(const char* str, uint64_t len, uint32_t* hash) {
    if (len == 0) {
        len = (uint64_t)strlen(str);
    }

    uint32_t h[5] = { 0x67452301 ,0xEFCDAB89 ,0x98BADCFE ,0x10325476 ,0xC3D2E1F0 };

    uint32_t w[80];
    for (uint64_t i = 0; i < 16; i++) {
        w[i] = 0;
    }
    for (uint64_t i = 0; i < len; i++) {
        w[i / 4] |= (uint32_t)(str[i]) << ((i % 4) * 8);
    }
    w[15] = (uint32_t)len * 8;

    for (uint64_t i = 16; i < 80; i++) {
        const uint32_t v = w[i - 3] ^ w[i - 8] ^ w[i - 14] ^ w[i - 16];
        w[i] = (v << 1) | (v >> 31);
    }

    uint32_t a = h[0];
    uint32_t b = h[1];
    uint32_t c = h[2];
    uint32_t d = h[3];
    uint32_t e = h[4];

    for (uint64_t i = 0; i < 80; i++) {
        uint32_t f = 0;
        uint32_t k = 0;
        if (i < 20) {
            f = (a & b) | (~b & d);
            k = 0x5A827999;
        }
        else if (i < 40) {
            f = b ^ c ^ d;
            k = 0x6ED9EBA1;
        }
        else if (i < 60) {
            f = (b & c) | (b & d) | (c & d);
            k = 0x8F1BBCDC;
        }
        else {
            f = b ^ c ^ d;
            k = 0xCA62C1D6;
        }

        const uint32_t t = ((a << 5) | (a >> 27)) + f + e + k + w[i];
        e = d;
        d = c;
        c = (b << 30) | (b >> 2);
        b = a;
        a = t;
    }

    h[0] = h[0] + a;
    h[1] = h[1] + b;
    h[2] = h[2] + c;
    h[3] = h[3] + d;
    h[4] = h[4] + e;

    hash[4] = h[0];
    hash[3] = h[1];
    hash[2] = h[2];
    hash[1] = h[3];
    hash[0] = h[4];
}

#define MOD_VAL (UINT64_C(1000000007))

typedef struct {
    uint64_t strListSize;
    char str[10][11];
} HMap;

static HMap hMap[1000000];

static int64_t P[5000], C[5000], cT[5000], cSumA[5000], cSecMax[5001], cChecked[5000];

int main(void) {
    int64_t N, K;

    scanf("%"PRId64"%"PRId64, &N, &K);
    for (int64_t i = 0; i < N; i++) {
        scanf("%"PRId64, &P[i]);
        P[i]--;
    }
    for (int64_t i = 0; i < N; i++) {
        scanf("%"PRId64, &C[i]);
        cChecked[i] = false;
    }

    int64_t r = INT64_MIN;

    for (int64_t i = 0; i < N; i++) {
        int64_t cSize = 0;

        int64_t cp = i;
        int64_t cSum = 0;
        while (!cChecked[cp]) {
            cT[cSize] = C[cp];
            cChecked[cp] = true;
            cSum += C[cp];

            //printf("sorted %"PRId64"\n", cT[cSize]);

            cp = P[cp];

            cSize++;
        }

        if (0 < cSize) {
            //printf("cSum %"PRId64"\n", cSum);

            for (int64_t i = 1; i <= cSize; i++) {
                cSecMax[i] = INT64_MIN;
            }

            for (int64_t i = 0; i < cSize; i++) {
                if (i == 0) {
                    cSumA[0] = cT[0];
                }
                else {
                    cSumA[i] = cSumA[i - 1] + cT[i];
                }

                //printf("s %"PRId64"\n", cSumA[i]);
            }

            for (int64_t k = 1; k <= cSize; k++) {
                for (int64_t i = 0; i < cSize; i++) {
                    const int64_t l = (i + cSize - 1) % cSize;
                    const int64_t r = (i + k - 1) % cSize;
                    if (l < r) {
                        cSecMax[k] = MAX(cSecMax[k], cSumA[r] - cSumA[l]);
                    }
                    else if (l == r) {
                        cSecMax[k] = MAX(cSecMax[k], cSumA[cSize - 1]);
                    }
                    else {
                        cSecMax[k] = MAX(cSecMax[k], cSumA[cSize - 1] - cSumA[l] + cSumA[r]);
                    }
                }

                //printf("cM %"PRId64"\n", cSecMax[k]);
            }

            int64_t cSecMaxMax = INT64_MIN;

            if (K < cSize) {
                for (int64_t k = 1; k <= K; k++) {
                    cSecMaxMax = MAX(cSecMaxMax, cSecMax[k]);
                }
            }
            else {
                if (cSum <= 0) {
                    for (int64_t k = 1; k <= cSize; k++) {
                        cSecMaxMax = MAX(cSecMaxMax, cSecMax[k]);
                    }
                }
                else {
                    if (K % cSize == 0) {
                        cSecMaxMax = 0;
                        for (int64_t k = 1; k <= cSize; k++) {
                            cSecMaxMax = MAX(cSecMaxMax, cSecMax[k]);
                        }

                        cSecMaxMax += cSum * ((K / cSize) - 1);
                    }
                    else {
                        cSecMaxMax = 0;
                        for (int64_t k = 1; k <= K % cSize; k++) {
                            cSecMaxMax = MAX(cSecMaxMax, cSecMax[k]);
                        }

                        cSecMaxMax += cSum * (K / cSize);
                    }
                }
            }

            //printf("cMM %"PRId64"\n", cSecMaxMax);

            r = MAX(r, cSecMaxMax);
        }
    }


    printf("%"PRId64, r);

    return 0;
}