20699.cpp

#include <bits/stdc++.h>
#define fastio ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0)

#define ll long long
using namespace std;

const ll INF = 1e9 + 7;
const ll DIV = 987654321;


int A, B;   // 2만 짝수개면 망함

array<int,3> ans[102020];
int cnt = 1;
int need[101010];

pair<int,int> di[101010];


bool go(int cur, int a, int b){

    if(need[b] > a) return 0;

    if(b){
        b--;
        ans[cur][0] = 2;
    }
    else{
        ans[cur][0] = 1;
        a--;
    }
    
    int lb = di[b].first, rb = di[b].second;
    int la = (lb < rb ? (rb - lb) * 2 - 1 : 0), ra = (lb > rb ? (lb - rb) * 2 - 1 : 0);
    
    if(la && a){
        la++;
        a--;
    }
    else if(ra && a){
        ra++;
        a--;
    }
    la += a /2;
    ra += (a + 1)/2;

    bool ret = 1;   
    if(la || lb){
        cnt++;
        ans[cur][1] = cnt;
        ret &= go(cnt, la, lb);
    }

    if(ra || rb){
        cnt++;
        ans[cur][2] = cnt;
        ret &= go(cnt ,ra, rb);
    }

   
    return ret;
}
int main()
{
    fastio;
    cin >> A >> B;
    need[1] = 0;
    need[2] = 1;
    need[0] = 0;
    di[1] = {0, 1};
    di[2] = {1, 1};

    for(int i = 3;i<= B;i++){
        int a = (i - 1) / 2, b = i / 2;
        
        need[i] = need[a] + need[b];
        if(i% 2 == 0) need[i]++;
        di[i] = {a, b};

        int t = need[i];

        for(int j = i - t;j<=i + t;j++){
            int k = i - 1 - j;
            if(j >=0 && k >=0){
                int val = need[j] + need[k] + abs(j - k) * 2 - 1;

                if(val < need[i]){
                    need[i] = need[j] + need[k] + abs(j - k) * 2 - 1;
                    di[i] = {j, k};
                }
            }
        }
    }

    
    if(go(1, A, B)){
        for(int i = 1;i<=A + B;i++){
            cout << ans[i][0] << " " << ans[i][1] << " " << ans[i][2] << "\n";
        }
    }
    else cout << -1;
    return 0;
}