#include<bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define ins insert
#define pq priority_queue
#define minele min_element
#define maxele max_element
#define lb lower_bound //first pos >= val
#define ub upper_bound // first pos > val
#define cnt_bit __builtin_popcount
#define debug(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx,avx2,fma")
using namespace std;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;


int d4x[4] = {1, 0, -1, 0}; int d4y[4] = {0, 1, 0, -1};
int d8x[8] = {0, 1, 1, 1, 0, -1, -1, -1};
int d8y[8] = {1, 1, 0, -1, -1, -1, 0, 1};

const ll oo = 1e18;
const ll maxN = 1e6;

/* Author : Le Ngoc Bao Anh, 10A5, LQD High School for Gifted Student */

void maximize(int &a, int b) {
    a = max(a, b);
}

void minimize(int &a, int b) {
    a = min(a, b);
}

ll MOD;
const int N = 1e6 + 100;
int n, k;
int sz[N];
int cnt[4][N], num[N];
ll f[N], invf[N], fact[N], ans[N];
vector<int> g[N];
vector<int> b[N];

ll Power(ll a, ll b, ll MOD) {
    if(b == 0) return 1;
    if(b == 1) return (a % MOD);
    ll T = Power(a, b / 2, MOD);
    if(b % 2) return (T * T % MOD * a % MOD);
    return (T * T % MOD);
}

int phi(int n) {
    int res = n;
    for (int i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            while (n % i == 0) {
                n /= i;
            }
            res -= res / i;
        }
    }
    if (n != 1) {
        res -= res / n;
    }
    return res;
}

void add(ll &x, ll y) {
    x = (x + y);
    if(x < 0) x += MOD;
    if(x >= MOD) x -= MOD;
}

void dfs(int u, int p) {
    sz[u] = 1;
    ans[u] = f[n - 1];
    for(auto v : g[u]) {
        if(v != p) {
            dfs(v, u);
            sz[u] += sz[v];
            add(ans[u], -f[sz[v]]);
        }
    }
    add(ans[u], -f[n - sz[u]]);
}

void solve() {
    //ans(u) = C(n - 1, k) - (v is son of u)C(chils(v), k) - C(n - child(u), k);
    //=> how to cal C(x, k)
    //C(x, k) = C(x - 1, k) * x / (x - k);
    //=> gcd(x, y) = 1 => x * c mod y = 1 (c = phi(y))
    cin >> n >> k >> MOD;

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

    if(MOD == 1019972207) {
        fact[0] = 1;
        invf[0] = 1;
        for(int i = 1; i <= n; i++) {
            fact[i] = fact[i - 1] * i % MOD;
            invf[i] = Power(fact[i], MOD - 2, MOD);
        }

        for(int i = k; i <= n; i++) {
            f[i] = fact[i] * invf[k] % MOD * invf[i - k] % MOD;
        }
    } else {
        vector<int> prime = {19, 127, 467, 907};
        int euler = phi(MOD);
        fact[0] = 1;
        invf[0] = 1;
        for(int i = 1; i <= n; i++) num[i] = i;
        for(int i = 0; i < 4; i++) {
            for(int j = 1; j <= n; j++) {
                cnt[i][j] = cnt[i][j - 1];
                while(num[j] % prime[i] == 0) {
                    num[j] /= prime[i];
                    cnt[i][j]++;
                }
            }
        }

        for(int i = 1; i <= n; i++) {
            fact[i] = fact[i - 1] * num[i] % MOD;
            invf[i] = Power(fact[i], euler - 1, MOD);
        }

        for(int i = k; i <= n; i++) {
            f[i] = fact[i] * invf[k] % MOD * invf[i - k] % MOD;
            for(int j = 0; j < 4; j++) {
                int b = cnt[j][i] - cnt[j][k] - cnt[j][i - k];
                f[i] = f[i] * Power(prime[j], b, MOD) % MOD;
            }
        }
    }

    dfs(1, 0);
    ll res = 0;
    for(int i = 1; i <= n; i++) add(res, ans[i]);
    cout << res;
}

int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #else
    //online
    #endif

    int tc = 1, ddd = 0;
    // cin >> tc;
    while(tc--) {
        //ddd++;
        //cout << "Case #" << ddd << ": ";
        solve();
    }
}