Kth Subtree

#include<bits/stdc++.h>

using namespace std;



#define fastio() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define MOD 1000000007
#define MOD1 998244353
#define INF 1e18
#define nline "\n"
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define ff first
#define ss second
#define PI 3.141592653589793238462
#define set_bits __builtin_popcountll
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()

typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
// typedef tree<pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update > pbds; // find_by_order, order_of_key

#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x)
#endif

void _print(ll t) {cerr << t;}
void _print(int t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(lld t) {cerr << t;}
void _print(double t) {cerr << t;}
void _print(ull t) {cerr << t;}

template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(pair <T, V> p) {cerr << "{"; _print(p.ff); cerr << ","; _print(p.ss); cerr << "}";}
template <class T> void _print(vector <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(set <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(multiset <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void _print(map <T, V> v) {cerr << "[ "; for (auto i : v) {_print(i); cerr << " ";} cerr << "]";}
int n;
ll k;
vector<vector<int>>g;
vector<vector<ll>>dp;
vector<int>child(5001,0);
void dfs(int u,int p){
    debug(u);
    for(int v:g[u]){
        if(v!=p){
            dfs(v,u);
            child[u]+=child[v];
            child[u]++;
        }
    }
    dp[u].resize(child[u]+2,0);
    dp[u][1]=1;
    for(int v:g[u]){
        if(v!=p){
            vector<ll>sum(child[u]+2);
            for(int num=child[u]+1;num>=1;num--){
                for(int i=0;i<=min(child[v]+1,num);i++){
                    // i nodes v ke use karo
                    // num-i nodes purane walo ke
                    dp[u][num]+=dp[v][i]*(dp[u][num-i]);
                }
                // sum[num]+=dp[u][num];
            }
        }
    }
    debug(u);
    debug(dp[u]);



}
int main() {
#ifndef ONLINE_JUDGE
    freopen("Error.txt", "w", stderr);
#endif
    cin>>n>>k;
    g.resize(n+1);
    dp.resize(n+1);
    for(int i=0;i<n-1;i++){
        int u,v;
        cin>>u>>v;
        g[u].pb(v);
        g[v].pb(u);
    }
    dfs(1,-1);
    vector<ll>cnt(n+1,0);
    for(int i=1;i<=n;i++){
        dp[i].resize(n+1);
        for(int j=1;j<=n;j++){
            cnt[j]+=dp[i][j];
        }
    }
    ll sub=0;
    ll ans=-1;
    for(int i=1;i<=n;i++){
        // cout<<cnt[i]<<"\n";
        if(sub<k){
            sub+=cnt[i];
        }
        if(sub>=k){
            ans=i;
            break;
        }
    }
    cout<<ans<<"\n";





}