#pragma GCC optimize ("O2")
#pragma GCC target ("avx2")
//#include<bits/stdc++.h>
//#include<atcoder/all>
//using namespace atcoder;
#include<iostream>
#include<cstring>

using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define rep1(i, n) for(int i = 1; i <= (n); i++)
#define co(x) cout << (x) << "\n"
#define cosp(x) cout << (x) << " "
#define ce(x) cerr << (x) << "\n"
#define cesp(x) cerr << (x) << " "
#define pb push_back
#define mp make_pair
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define Would
#define you
#define please

const int CM = 1 << 17, CL = 12;
char cn[CM + CL], * ci = cn + CM + CL, * owa = cn + CM, ct;
const ll ma0 = 1157442765409226768;
const ll ma1 = 1085102592571150095;
const ll ma2 = 71777214294589695;
const ll ma3 = 281470681808895;
const ll ma4 = 4294967295;
inline int getint() {
	if (ci - owa > 0) {
		memcpy(cn, owa, CL);
		ci -= CM;
		fread(cn + CL, 1, CM, stdin);
	}
	ll tmp = *(ll*)ci;
	int dig = 68 - __builtin_ctzll((tmp & ma0) ^ ma0);
	tmp = tmp << dig & ma1;
	tmp = tmp * 10 + (tmp >> 8) & ma2;
	tmp = tmp * 100 + (tmp >> 16) & ma3;
	tmp = tmp * 10000 + (tmp >> 32) & ma4;
	ci += 72 - dig >> 3;
	return tmp;
}
const int MAX = 1000;
class shuturyoku_unko {
public:
	char C[MAX * 4];
	constexpr shuturyoku_unko() : C() {
		rep(i, MAX) {
			int X = i;
			rep(j, 3) {
				C[i * 4 + 2 - j] = '0' + X % 10;
				X /= 10;
			}
			C[i * 4 + 3] = ' ';
		}
	}
};
constexpr shuturyoku_unko f;
const int dm = 1 << 17;
char* dn = cn, * di = dn, * owad = dn + dm - 20;
void putint(int A) {
	if (owad < di) {
		fwrite(dn, 1, di - dn, stdout);
		di = dn;
	}
	if (A >= 1000) {
		int dig = 1;
		if (A >= 100000) dig = 3;
		else if (A >= 10000) dig = 2;
		memcpy(di, f.C + A / 1000 * 4 + 3 - dig, dig);
		memcpy(di + dig, f.C + A % 1000 * 4, 4);
		di += dig + 4;
	}
	else {
		int dig = 1;
		if (A >= 100) dig = 3;
		else if (A >= 10) dig = 2;
		memcpy(di, f.C + A * 4 + 3 - dig, dig + 1);
		di += dig + 1;
	}
}

int N;
int to[400001], ne[400001], he[200001];
int Q[200001], vis[200001], p, q;
ll are[200001];

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);


	N = getint();
	rep1(i, N * 2 - 2) {
		int a = getint(), b = getint();
		to[i] = b;
		ne[i] = he[a];
		he[a] = i++;
		to[i] = a;
		ne[i] = he[b];
		he[b] = i;
	}

	Q[q++] = 1;
	while (p < q) {
		int u = Q[p++];
		vis[u] = -1;
		for (int i = he[u]; i; i = ne[i]) {
			if (vis[to[i]] == 0) {
				Q[q++] = to[i];
			}
		}
	}
	int tmp = Q[N - 1];
	p = 0;
	q = 0;
	Q[q++] = tmp;
	vis[tmp] = 0;
	while (p < q) {
		int u = Q[p++];
		int mae = 0;
		for (int i = he[u]; i; i = ne[i]) {
			if (vis[to[i]] < 0) {
				vis[to[i]] = u;
				Q[q++] = to[i];
				mae = i;
			}
			else {
				if (mae) ne[mae] = ne[i];
				else he[u] = ne[i];
			}
		}
	}
	ll m = (1ll << 20) - 1, m0 = ~m, m1 = 1ll << 20;
	for (int i = N - 1; i >= 0; i--) {
		int u = Q[i];
		ll kari = (are[u] & m0) + m1 + u;
		if (are[vis[u]] < kari) are[vis[u]] = kari;
	}

	int k = 0;
	q = 0;
	Q[q++] = tmp;
	while (q) {
		k++;
		int u = Q[q - 1];
		if (u < 0) q--;
		else {
			vis[u] = -k;
			Q[q - 1] = -u;
			int nanika = are[u] & m;
			if (nanika) Q[q++] = nanika;
			for (int i = he[u]; i; i = ne[i]) {
				int v = to[i];
				if (v != nanika) {
					Q[q++] = v;
				}
			}
		}
	}

	rep1(i, N) putint(-vis[i]);
	fwrite(dn, 1, di - dn, stdout);

	Would you please return 0;
}
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define per(i, n) for (int i = n - 1; i >= 0; i--)
#define per1(i, n) for (int i = n; i >= 1; i--)
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define pbp(f, s) pb(mp(f, s));
using namespace std;
typedef long long int ll;
typedef pair<int, int> PI;
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
/*--------------------------------------------------*/
string x;
ll m;
/*--------------------------------------------------*/
void speedUpIO() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
}

bool check(ll p) {
    V<ll> y;
    ll mm = m;
    while (mm > 0) {
        y.pb(mm % p);
        mm /= p;
    }
    reverse(all(y));
    if (x.size() < y.size()) return true;
    if (x.size() > y.size()) return false;
    rep(i, x.size()) {
        if (x[i] - '0' < y[i]) return true;
        if (x[i] - '0' > y[i]) return false;
    }
    return true;
}

int main() {
    speedUpIO();

    cin >> x >> m;
    if (x.size() == 1) {
        int xi = stoi(x);
        cout << (xi <= m ? 1 : 0) << "\n";
        return 0;
    }
    int d = 0;
    for (char c : x) d = max(d, c - '0');
    ll ok = d;
    ll ng = m + 1;
    // ll ng = 1e18 + 1;
    while (ng - ok > 1) {
        ll mid = ok / 2 + ng / 2;
        if (ok % 2 == 1 && ng % 2 == 1) mid++;
        if (check(mid))
            ok = mid;
        else
            ng = mid;
    }
    cout << ok - d << "\n";
    return 0;
}