#include <iostream>
#include <vector>
#include <algorithm>
#include <array>
#include <sstream>
using namespace std;
constexpr int siz = 51;
typedef array<long long int, siz> poly;
poly& operator +=(poly &a, const poly &b){
    for(int i=0; i<siz; i++){
        a[i] += b[i];
    }
    return a;
}
poly& operator -=(poly &a, const poly &b){
    for(int i=0; i<siz; i++){
        a[i] -= b[i];
    }
    return a;
}

template <typename T>
struct MaxFlow{
    struct edge{
        int to, rev;
        T cap;
        edge(int t, int r, T c):to(t),rev(r),cap(c){
            cap = c;
        }
        edge(){}
    };
    vector<vector<edge>> graph;
    T zero;
    T inf;
    
    MaxFlow(int n, T zero, T inf):zero(zero),inf(inf){
        graph.resize(n);
    }
    void add_edge(int from, int to, T cap){
        graph[from].emplace_back(to, graph[to].size(), cap);
        graph[to].emplace_back(from, (int)graph[from].size()-1, zero);
    }
    void add_bidirectional_edge(int from, int to, T cap){
        graph[from].emplace_back(to, graph[to].size(), cap);
        graph[to].emplace_back(from, (int)graph[from].size()-1, cap);
    }
    T dfs(int v, int g, T flow, vector<bool>& used){
        if(used[v]) return zero;
        used[v] = true;
        if(v == g) return flow;
    
        for(auto &e: graph[v]){
            if(zero < e.cap){
                T ret = dfs(e.to, g, min(flow, e.cap), used);
                if(zero < ret){
                    e.cap -= ret;
                    graph[e.to][e.rev].cap += ret;
                    return ret;
                }
            }
        }
        return zero;
    }
    T exec(int s, int g){
        T res = zero;
        while(1){
            vector<bool> used(graph.size(), false);
            T ret = dfs(s, g, inf, used);
            if(ret == zero) break;
            res += ret;
        }
        return res;
    }
};

poly str2poly(string s){
    for(char &c: s){
        if(c == '+') c = ' ';
    }
    stringstream ss(s);
    poly res{};
    string t;
    while(ss >> t){
        int n = t.length();
        int xpos = find(t.begin(), t.end(), 'x') -t.begin();
        if(xpos == n){
            res[siz-1] = stoi(t);
            continue;
        }
        int coef = 1;
        if(xpos != 0) coef = stoi(t.substr(0, xpos));
        int deg = 1;
        if(xpos != n-1) deg = stoi(t.substr(xpos+2, n-(xpos+2)));
        res[siz-1-deg] = coef;
    }
    return res;
}
string poly2str(const poly &p){
    string res = "";
    for(int i=0; i<siz; i++){
        if(p[i] == 0) continue;
        if(p[i]>0 and res!="") res += "+";
        if(i < siz-1){
            if(p[i] == -1){
                res += "-";
            }else if(p[i] != 1){
                res += to_string(p[i]);
            }
        }else{
            res += to_string(p[i]);
        }
        if(i==siz-1) continue;
        res += "x";
        if(i==siz-2) continue;
        res += "^" + to_string(siz-1-i);
    }
    if(res == "") res = "0";
    return res;
}

int main(){
    poly zero{}, inf;
    for(int i=0; i<siz; i++){
        inf[i] = 1e9;
    }
    while(1){
        int n,m;
        cin >> n >> m;
        if(n == 0) break;

        MaxFlow<poly> mf(n, zero, inf);
        for(int i=0; i<m; i++){
            int u,v;
            string s;
            cin >> u >> v >> s;
            u--; v--;
            mf.add_bidirectional_edge(u, v, str2poly(s));
        }
        poly ret = mf.exec(0, n-1);
        cout << poly2str(ret) << endl;
    }    
    return 0;
}



Measured memory_bytes: 3880