#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <cfloat>
#include <ctime>
#include <cassert>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <numeric>
#include <list>
#include <iomanip>
#include <fstream>
#include <bitset>
   
using namespace std;
   
 
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define foreach(it, c) for (__typeof__((c).begin()) it=(c).begin(); it != (c).end(); ++it)
#define rforeach(it, c) for (__typeof__((c).rbegin()) it=(c).rbegin(); it != (c).rend(); ++it)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define CL(arr, val) memset(arr, val, sizeof(arr))
#define COPY(dest, src) memcpy(dest, src, sizeof(dest))
#define ten(n) ((long long)(1e##n))
#define bin(n) (1LL << (n))
#define erep(i, n) for (int i = 0; i <= (int)(n); ++i)
#define revrep(i, n) for (int i = (n); i >= 0; --i)
#define pb push_back

template <class T> void chmax(T& a, const T& b) { a = max(a, b); }
template <class T> void chmin(T& a, const T& b) { a = min(a, b); }

template <class T> T round_up(T a, T b) { return (a + b - 1) / b; }

template <class T> void uniq(vector<T>& c) { sort(c.begin(), c.end()); c.erase(unique(c.begin(), c.end()), c.end()); }
 
template <class T> string to_s(const T& a) { ostringstream os; os << a; return os.str(); }
template <class T> T to_T(const string& s) { istringstream is(s); T res; is >> res; return res; }
  
template <class T, class U> ostream& operator<<(ostream& os, pair<T, U>& p) { os << "( " << p.first << ", " << p.second << " )"; return os; }
  
template <class T> void print(T a, int n, const string& deli = " ", int br = 1) { for (int i = 0; i < n; ++i) { cout << a[i]; if (i + 1 != n) cout << deli; } while (br--) cout << endl; }
template <class T> void print(const T& c, const string& deli = " ", int br = 1) { foreach (it, c) { cout << *it; if (++it != c.end()) cout << deli;--it; } while (br--) cout << endl; }
template <class T> void print2d(T a, int w, int h, int width = -1, int br = 1) { for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) {    if (width != -1) cout.width(width); cout << a[i][j] << ' '; } cout << endl; } while (br--) cout << endl; }
   
template <class T> void input(T& a, int n) { for (int i = 0; i < n; ++i) cin >> a[i]; }
template <class T> void input(T* a, int n) { for (int i = 0; i < n; ++i) cin >> a[i]; }

void fix_pre(int n) { cout.setf(ios::fixed, ios::floatfield); cout.precision(10); }
void fast_io() { cin.tie(0); ios::sync_with_stdio(false); }
#define trace(x) (cout << #x << ": " << (x) << endl)
 
bool in_rect(int x, int y, int w, int h) { return 0 <= x && x < w && 0 <= y && y < h; }
 

typedef long long ll;
typedef pair<int, int> pint;
 
// y(v): v>^<  y(^): ^>v<
const int dx[] = { 0, 1, 0, -1 };
const int dy[] = { 1, 0, -1, 0 };

const double PI = acos(-1.0);

#define F first
#define S second



vector<string> split(string str, const string& deli_chars)
{
    for (int i = 0; i < str.size(); ++i)
        if (deli_chars.find(str[i]) != string::npos)
            str[i] = ' ';
    stringstream ss(str);
    vector<string> res;
    for (string s; ss >> s; )
        res.push_back(s);
    return res;
}
ll ext_gcd(ll a, ll b, ll &x, ll &y)
{
    if (b)
    {
        ll g = ext_gcd(b, a % b, y, x);
        y -= (a / b) * x;
        return g;
    }
    else
    {
        x = 1, y = 0;
        return a;
    }
}
ll mod_inverse(ll a, ll mod)
{
    ll x, y;
    if (ext_gcd((a + mod) % mod, mod, x, y) == 1)
        return (mod + x % mod) % mod;
    else
        return 0;
}


ll mod;
bool error;
int pos;
string s;
void init(const string& s, int p)
{
    ::s = s;
    pos = 0;
    error = false;
    mod = p;
}
ll expr();
ll factor();
ll term();
ll add(ll a, ll b)
{
    return (a + b) % mod;
}
ll sub(ll a, ll b)
{
    return (a - b + mod) % mod;
}
ll mul(ll a, ll b)
{
    return a * b % mod;
}
ll divi(ll a, ll b)
{
    if (b == 0)
    {
        error = true;
        return 0;
    }
    return a * mod_inverse(b, mod) % mod;
}
ll expr()
{
    ll res = factor();
    while (pos < s.size() && s[pos] == '+' || s[pos] == '-')
    {
        if (s[pos] == '+')
        {
            ++pos;
            res = add(res, factor());
        }
        else
        {
            ++pos;
            res = sub(res, factor());
        }
    }
    return res;
}
ll factor()
{
    ll res = term();
    while (s[pos] == '*' || s[pos] == '/')
    {
        if (s[pos] == '*')
        {
            ++pos;
            res = mul(res, term());
        }
        else
        {
            ++pos;
            res = divi(res, term());
        }
    }
    return res;
}
ll term()
{
    if (s[pos] == '(')
    {
        ++pos;
        ll res = expr();
        assert(s[pos] == ')');
        ++pos;
        return res;
    }
    else
    {
        assert(isdigit(s[pos]));
        ll res = 0;
        while (isdigit(s[pos]))
        {
            res = res * 10 + (s[pos] - '0');
            ++pos;
        }
        return res;
    }
}
string cat(string s)
{
    stringstream ss(s);
    string res;
    while (ss >> s)
        res += s;
    return res;
}
int main()
{
    string in;
    while (getline(cin , in) && in[0] != '0')
    {
        in = cat(in);
        int w = in.find(':');
        int p = to_T<int>(in.substr(0, w));
        string s = in.substr(w + 1);

        init(s, p);
        int res = expr();
        if (error)
            puts("NG");
        else
            printf("%s = %d (mod %d)\n", s.c_str(), res, p);
    }
}

Measured memory_bytes: 1588