LCAHLD.cpp

/************************************************************************************

    Finding LCA (Least common ancestor) of two vertices in the tree.
    Uses heavy-light decomposition. 
    O(N) for preprocessing, O(logN) on query.

    Based on problem 111796 from informatics.mccme.ru 
    http://informatics.mccme.ru/moodle/mod/statements/view.php?chapterid=111796

************************************************************************************/

#include <iostream>
#include <fstream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cassert>
#include <utility>
#include <iomanip>

using namespace std;

const int MAXN = 105000;

int n, qn;
vector <int> g[MAXN];   
int tin[MAXN], tout[MAXN];
int p[MAXN];
int sz[MAXN];
int chain[MAXN], chainRoot[MAXN]; 
int chainNum;
int timer;

int a[2 * MAXN];
int x, y, z;

long long ans;

void dfs(int v, int par = -1) {
    timer++;
    tin[v] = timer;
    p[v] = par;
    sz[v] = 1;

    for (int i = 0; i < (int) g[v].size(); i++) {
        int to = g[v][i];
        if (to == par)
            continue;
        dfs(to, v);
        sz[v] += sz[to];
    }

    timer++;
    tout[v] = timer;    
}

bool isHeavy(int from, int to) {
    return 2 * sz[to] >= sz[from];
}

int newChain(int root) {
    chainNum++;
    chainRoot[chainNum] = root;
    return chainNum;
}

void buildHLD(int v, int curChain) {
    chain[v] = curChain;
    for (int i = 0; i < g[v].size(); i++) {
        int to = g[v][i];
        if (to == p[v])
            continue;
        if (isHeavy(v, to))
            buildHLD(to, curChain);
        else
            buildHLD(to, newChain(to));
    }
}

bool isParent(int a, int b) {
    return tin[a] <= tin[b] && tout[a] >= tout[b];
}

int lca(int a, int b) {
    while (true) {
        int curChain = chain[a];
        if (isParent(chainRoot[curChain], b))
            break;
        a = p[chainRoot[curChain]]; 
    }
    while (true) {
        int curChain = chain[b];
        if (isParent(chainRoot[curChain], a))
            break;
        b = p[chainRoot[curChain]];
    }
    if (isParent(a, b))
        return a;
    else
        return b;
}

int main() {
    //assert(freopen("input.txt","r",stdin));
    //assert(freopen("output.txt","w",stdout));  

    scanf("%d %d", &n, &qn);

    for (int i = 1; i < n; i++) {
        int par;
        scanf("%d", &par);
        par++;
        g[i + 1].push_back(par);
        g[par].push_back(i + 1);
    }

    dfs(1);
    buildHLD(1, newChain(1));

    // Reference problem input format
    scanf("%d %d", &a[1], &a[2]);
    scanf("%d %d %d", &x, &y, &z);
    for (int i = 3; i <= 2 * qn; i++) {
        a[i] = (1ll * x * a[i - 2] + 1ll * y * a[i - 1] + 1ll * z) % n;
    }

    int q1 = a[1], q2 = a[2]; 
    for (int i = 1; i <= qn; i++) {
        int cur = lca(q1 + 1, q2 + 1) - 1;
        ans += cur;
        q1 = (a[2 * (i + 1) - 1] + cur) % n;
        q2 = a[2 * (i + 1)];
    }

    cout << ans << endl;

    return 0;
}