D. Distance in Tree

// Problem: D. Distance in Tree
// Contest: Codeforces - VK Cup 2012 Round 1
// URL: https://codeforces.com/contest/161/problem/D
// Memory Limit: 512 MB
// Time Limit: 3000 ms
// Parsed on: 10-09-2021 11:19:46 IST (UTC+05:30)
// Author: Kapil Choudhary
// ********************************************************************
// कर्मण्येवाधिकारस्ते मा फलेषु कदाचन |
// मा कर्मफलहेतुर्भूर्मा ते सङ्गोऽस्त्वकर्मणि || १.४७ ||
// ********************************************************************

#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define ld long double
#define ull unsigned long long
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define F first
#define S second
#define PI 3.1415926535897932384626
#define sz(x) ((int)(x).size())
#define vset(v, n, val) v.clear(); v.resize(n, val)

typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef vector<vull> vvull;
typedef vector<vb> vvb;
typedef vector<vc> vvc;
typedef vector<vs> vvs;

/************************************************** DEBUGGER *******************************************************************************************************/

#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(ld 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(vector <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.F); cerr << ","; _print(p.S); cerr << "}"; }
template <class T> void _print(vector <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
template <class T> void _print(vector <vector<T>> v) { cerr << "==>" << endl; for (vector<T> vec : v) { for(T i : vec) {_print(i); cerr << " "; } cerr << endl; } }
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 << "]"; }

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

mt19937_64 rang(chrono::high_resolution_clock::now().time_since_epoch().count());
int rng(int lim) {
    uniform_int_distribution<int> uid(0,lim-1);
    return uid(rang);
}

const int INF = 0x3f3f3f3f;
const int mod = 1e9+7;

ll mod_exp(ll a, ll b) { a %= mod; if(a == 0) return 0LL; ll res = 1LL;
                         while(b > 0) { if(b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; }

ll mod_inv(ll a) { return mod_exp(a, mod - 2); } // works only for prime value of "mod"
ll GCD(ll a, ll b) { return (b == 0) ? a : GCD(b, a % b); }

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

vvi g;

// NOTE: this dp[][] will not calculate the actual result, but will help us
//       in reaching the overall answer.

// dp[i][k] = #nodes (in the subtree rooted at node i) which are exactly at
//            distance k from i
int dp[50001][501];

// #vertices, k value
int n, k;

// final result
ll res;

void dfs(int cur, int par) {
    // base case (not only for leaves but for all nodes)
    // the node at distance 0 will be the node itself
    dp[cur][0] = 1;

    // calculate dp[][] values for all the children of cur node
    for(auto x: g[cur]) {
        if(x == par) continue;
        dfs(x, cur);
    }

    // now, compute dp[][] values of cur node with help of it's children
    for(auto x: g[cur]) {
        if(x == par) continue;
        for(int d = 1; d <= k; d++) {
            dp[cur][d] += dp[x][d-1];
        }
    }

    // helper code to find overall result
    res += dp[cur][k];
    ll tmp = 0LL;

    for(auto x: g[cur]) {
        if(x == par) continue;
        for(int d = 1; d <= (k - 1); d++) {
            tmp += (dp[x][d - 1] * (dp[cur][k - d] - dp[x][k - d - 1]));
        }
    }

    res += (tmp / 2LL);
}

// https://www.youtube.com/watch?v=de2NZ2maFO0&list=PLzVLIdIx9dQxCKaiktxELrtXtnItgAAIr&index=9
void solve()
{
    cin >> n >> k;

    vset(g, n + 1, vi(0));
    memset(dp, 0, sizeof dp);
    res = 0LL;

    for(int i = 1; i < n; i++) {
        int x, y; cin >> x >> y;
        g[x].pb(y);
        g[y].pb(x);
    }

    dfs(1, 0);

    cout << res << "\n";
}

int main()
{
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    srand(chrono::high_resolution_clock::now().time_since_epoch().count());

    // #ifndef ONLINE_JUDGE
    //     freopen("input.txt", "r", stdin);
    //     freopen("output.txt", "w", stdout);
    // #endif

    // #ifndef ONLINE_JUDGE
    //      freopen("error.txt", "w", stderr);
    // #endif

    int t = 1;
    // int test = 1;
    // cin >> t;
    while(t--) {
        // cout << "Case #" << test++ << ": ";
        solve();
    }

    return 0;
}