#include <iostream>
#include <algorithm>
#include <queue>

typedef long long ll;
typedef double lf;

// #define DEBUG 1
struct IO
{
    #define MAXSIZE (1 << 20)
    #define isdigit(x) (x >= '0' && x <= '9')
    char buf[MAXSIZE], *p1, *p2;
    char pbuf[MAXSIZE], *pp;
    #if DEBUG
    #else
    IO() : p1(buf), p2(buf), pp(pbuf) {}
    ~IO() {fwrite(pbuf, 1, pp - pbuf, stdout);}
    #endif
    #define gc() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) ? ' ' : *p1++)
    #define blank(x) (x == ' ' || x == '\n' || x == '\r' || x == '\t')

    template <typename T>
    void Read(T &x)
    {
        #if DEBUG
        std::cin >> x;
        #else
        bool sign = 0; char ch = gc(); x = 0;
        for (; !isdigit(ch); ch = gc())
            if (ch == '-') sign = 1;
        for (; isdigit(ch); ch = gc()) x = x * 10 + (ch ^ 48);
        if (sign) x = -x;
        #endif
    }
    void Read(char *s)
    {
        #if DEBUG
        std::cin >> s;
        #else
        char ch = gc();
        for (; blank(ch); ch = gc());
        for (; !blank(ch); ch = gc()) *s++ = ch;
        *s = 0;
        #endif
    }
    void Read(char &c) {for (c = gc(); blank(c); c = gc());}

    void Push(const char &c)
    {
        #if DEBUG
        putchar(c);
        #else
        if (pp - pbuf == MAXSIZE) fwrite(pbuf, 1, MAXSIZE, stdout), pp = pbuf;
        *pp++ = c;
        #endif
    }
    template <typename T>
    void Write(T x)
    {
        if (x < 0) x = -x, Push('-');
        static T sta[35];
        int top = 0;
        do sta[top++] = x % 10, x /= 10; while (x);
        while (top) Push(sta[--top] ^ 48);
    }
    template <typename T>
    void Write(T x, char lst) {Write(x), Push(lst);}
} IO;
#define Read(x) IO.Read(x)
#define Write(x, y) IO.Write(x, y)
#define Put(x) IO.Push(x)

using namespace std;

const int MAXN = 5e4 + 10;

int n, m, k, s[MAXN]; ll ans[MAXN];
vector <int> e[MAXN];

char tp[MAXN]; int val[MAXN];

int dis[MAXN], cnt[MAXN];
inline void BFS1(int S)
{
    static queue <int> q;
    for (int i = 1; i <= n; i++) dis[i] = -1, cnt[i] = 0;
    dis[S] = 0, q.push(S);
    while (!q.empty())
    {
        int u = q.front(); q.pop();
        if (u != S && tp[u] == '1') cnt[u]++;
        for (auto v : e[u])
            if (dis[v] == -1)
                dis[v] = dis[u] + 1, cnt[v] = cnt[u], q.push(v);
            else if (dis[v] == dis[u] + 1) cnt[v] = max(cnt[v], cnt[u] + (tp[v] == '1'));
    }
}

ll sum[MAXN];

ll d[MAXN];
inline void BFS2(int s, int x)
{
    static queue <int> q[2];
    for (int i = 1; i <= n; i++) d[i] = 1e18, dis[i] = cnt[i] = 0;
    d[s] = 0, q[0].push(s);
    while (!q[0].empty() || !q[1].empty())
    {
        int u;
        if (q[1].empty() || (!q[0].empty() && d[q[0].front()] < d[q[1].front()])) u = q[0].front(), q[0].pop();
        else u = q[1].front(), q[1].pop();
        for (auto v : e[u])
            if (d[v] > d[u] + 1)
            {
                d[v] = d[u] + 1, dis[v] = dis[u] + 1, cnt[v] = cnt[u];
                if (tp[v] == '1') cnt[v]++, d[v] += x, q[1].push(v);
                else q[0].push(v);
            }
    }
}

int main()
{
    // freopen("04-02.in", "r", stdin);
    // freopen("A.out", "w", stdout);
    #if DEBUG
    #else
    ios::sync_with_stdio(0), cin.tie(0);
    #endif
    Read(n), Read(m), Read(k);
    for (int i = 1, u, v; i <= m; i++) Read(u), Read(v), e[u].push_back(v), e[v].push_back(u);
    Read(tp + 1);
    for (int i = 1; i <= k; i++) Read(s[i]);

    for (int i = 1; i <= n; i++)
        if (tp[i] == '1')
        {
            val[i] = 2;
            for (auto v : e[i])
                if (tp[v] == '1') { val[i] = 1; break; }
        }

    for (int i = 2; i <= k; i++)
    {
        BFS1(s[i]);
        int mn[3] = {0, (int)2e9, (int)2e9};
        for (int j = 1; j <= n; j++)
            if (tp[j] == '1' && j != s[i])
                mn[val[j]] = min(mn[val[j]], dis[j]);
        if (tp[s[i]] == '1') mn[val[s[i]]] = min(mn[val[s[i]]], 2);
        int cc = 2e9;
        for (int j = 1; j <= n; j++)
            if (val[j] == 1 && mn[1] == dis[j]) cc = min(cc, cnt[j]);
        for (int j = 1; j <= n; j++)
        {
            int cur = min(j + mn[1] - 1, 2 * j + mn[2] - 2);
            if (j > cc) cur = min(cur, j - cc + mn[1]);
            sum[j] += cur;
        }
    }

    for (int i = 1; i <= n; i++) ans[i] = 1e18; ans[s[1]] = 0;
    for (int i = 0; i <= n; i++)
    {
        BFS2(s[1], i);
        for (int j = 1; j <= n; j++)
            if (j != s[1]) ans[j] = min(ans[j], sum[cnt[j] - (tp[j] == '1')] + dis[j]);
    }
    for (int i = 1; i <= n; i++) cout << ans[i] << '\n';
    return 0;
}