#include <iostream>
#include <algorithm> // for sort, mainly
#include <vector>
#include <map>
#include <set>
#include <cmath>
#include <array>
#include <string>
#include <cstdio>
#include <iterator>
#include <unordered_set>
#include <cstdint> // for int64_t, int32_t, etc
#include <queue>
#include <stack>
#include <deque>
#include <numeric> // gcd, lcm
#include <fstream>
#include <bitset> // for bitset
#include <iomanip>
#include <cassert> // for set with custom ordering
#include <type_traits> // for set with custom ordering
#include <utility> // for swap, forward, etc
using namespace std;

#pragma GCC optimize("O2")
// #pragma GCC optimize("O1","O2","O3","Ofast","unroll-loops")
// #pragma GCC target("sse","sse2","sse3","sse4.1","sse4.2","avx","avx2","fma")

template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { os << '{'; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << '}'; }
void dbg_out() { cout << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cout << ' ' << H; dbg_out(T...); }
#ifdef LOCAL
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

/*

notes:

int64_t
stoi(string s) -> string to int
to_string() -> int (or else) to string

vector declaration:
vector<ll> v(n, 0)
vector<vector<ll>> v(n, vector<ll>(n, 0));

{if statement} ? {truth value} : {false value}

#ifdef LOCAL
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
#endif

std::lcm(ll a, ll b), std::gcd(int a, int b)

cout << fixed << setprecision(n);

set with custom ordering
set<ll, decltype(&cmp)> qu(cmp);

*/

typedef int64_t ll;

bool check(ll mx, ll k, ll n, vector<ll> &p, vector<ll> &pd, vector<vector<ll>> &ch, vector<bool> leaf, vector<ll> in) {

    // megnezzuk, hany elet kene-e levagjunk
    // hogy a maximum x vagy kisebb legyen
    // ha ez a szam nagyobb mint k, nem lehet
    // ha kisebb, lehet

    // megyunk top-down
    // megnezzuk, ha egy gyerektol tul nagy lenne az ido
    // akkor azt levagjuk, nyissz

    ll cuts = 0;

    /*
    
    es itt az a kerdes, hogy fentrol lefele megyunk-e
    es en azt mondom, lentrol felfele
    mert figyelj ide:

              1
            /  \
           2    5
         /  \    \ 
        3   4     6

        minden el sulya 10
        ha fentrol jovunk, es mohon vesszuk
        akkor k = 2-re nem jon ki
        mert elvagja a 2-3, 2-4-et
        es aztan nem marad az 1-5-re

        de ha lentrol jovunk
        elvagja az 1-2-et, es az 1-5-t

    */
    
    vector<ll> dh(n+1, 0);

    queue<ll> q;
    for(ll i = 1; i <= n; i++) {
        if(leaf[i]) {
            q.push(i);
        }
    }

    while(!q.empty()) {

        ll curr = q.front();
        q.pop();

        // ha innen a szulojeig, tobb lenne mint mx, akkor kell egy cut

        if(dh[curr] + pd[curr] > mx) {
            cuts++;
        }else{
            dh[p[curr]] = max(dh[p[curr]], dh[curr] + pd[curr]);
        }

        in[p[curr]]--;
        if(in[p[curr]] == 0) {
            q.push(p[curr]);
        }
    }

    if(cuts <= k) {
        return true;
    }else{
        return false;
    }
}

void solve() {

	ll n, k;
	cin >> n >> k;
    vector<ll> p(n+1, 0); // parent
    vector<ll> pd(n+1, 0); // parent distance	
	vector<vector<ll>> ch(n+1); // children count

    vector<ll> in(n+1, 0);

	vector<bool> leaf(n+1, true); // stores for each whether it's a leaf

	for(ll i = 2; i <= n; i++) {
		cin >> p[i] >> pd[i];

        in[p[i]]++;

		leaf[p[i]] = false;
		ch[p[i]].push_back(i);
	}

    // let's do a binary search
    // why not
    // (I checked someone else's solution)

    // binary search for the smallest value which we can achieve
    // using k or less cuts
    // this is a first

    if(k == n - 1) {
        cout << "0\n";
        return;
    }
    // eset lekezelve

    // l biztos nem lehet, r biztos lehet
    // first true binary search
    ll l = 0, r = 1e18;
    while(l < r) {

        //cerr << "\nl=" << l << "; r=" << r;

        ll mid = l + (r - l)/2;
        if(check(mid, k, n, p, pd, ch, leaf, in)) {
            r = mid;
        }else{
            l = mid+1;
        }
    }

    //cerr << "\nl=" << l;

    cout << l;

}	

int main()
{
	std::ios_base::sync_with_stdio(false);
	//cin.tie(nullptr);
	//cout.tie(nullptr);

	solve();

	return 0;
}