Codeforces-solutions/Educational Codeforces Round 37 (Rated for Div. 2)/D. Tanks.cpp

/* Problem URL: https://codeforces.com/contest/920/problem/D */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

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

    int n, k;
    ll v;
    cin >> n >> k >> v;

    vl a(n);
    cin >> a;

    if (v == 0) {
        cout << "YES\n";
        cout << (ll)1e9 << ' ' << 1 << ' ' << 2 << '\n';
        return 0;
    }

    if (accumulate(all(a), 0LL) < v) {
        cout << "NO\n";
        return 0;
    }

    auto printans = [&](V<tuple<ll, int, int>> &ans) {
        for (auto [c, i, j] : ans) {
            if (c == 0) {
                continue;
            }

            cout << c << ' ' << i << ' ' << j << '\n';
        }
    };

    ll mod = v % k;
    vi ans;

    if (mod == 0) {
        cout << "YES\n";
        V<tuple<ll, int, int>> lol;

        int choice = 0;
        int other = 1;

        nrep(i, 1, n) {
            lol.emplace_back(1e9, i + 1, choice + 1);
        }

        lol.emplace_back(v / k, choice + 1, other + 1);

        printans(lol);
        return 0;
    }

    ll oo = INT64_MAX >> 1;

    V<V<bool>> dp(n + 1, V<bool>(k));

    nrep(i, 1, n + 1) {
        dp[i][a[i - 1] % k] = true;
        rep(j, k) {
            dp[i][j] = dp[i][j] || dp[i - 1][j] || dp[i - 1][((j - a[i - 1]) % k + k) % k];
        }
    }

    auto getans1 = [&](ll mod) {
        if (!dp[n][mod]) {
            return false;
        }

        int ind = n - 1;
        int act = mod;
        while (ind >= 0) {
            while (dp[ind][act]) {
                ind--;
            }

            if (!dp[ind + 1][act]) {
                break;
            }

            ans.push_back(ind);
            act = ((act - a[ind]) % k + k) % k;
            ind--;
        }

        return !ans.empty();
    };

    if (!getans1(mod)) {
        cout << "NO\n";
        return 0;
    }

    if (ans.empty()) {
        cout << "NO\n";
        return 0;
    }
    //
    // if (ans.size() == 1) {
    //     ll total = a[ans[0]];
    //     V<tuple<ll, int, int>> lol;
    //
    //     ll other = ans[0] == 0 ? 1 : 0;
    //
    //     rep(i, n) {
    //         if (i == ans[0]) {
    //             continue;
    //         }
    //
    //         lol.emplace_back(a[i] / k, i + 1, ans[0] + 1);
    //         total += (a[i] / k) * k;
    //     }
    //
    //     if (total < v) {
    //         cout << "NO\n";
    //         return 0;
    //     }
    //
    //     cout << "YES\n";
    //     ll diff = total - v;
    //     lol.emplace_back(diff / k, ans[0] == 0 ? 2 : 1, ans[0] + 1);
    //     printans(lol);
    //
    //     return 0;
    // }
    //
    V<tuple<ll, int, int>> lol;

    set<int> ignore;
    ignore.insert(ans[0]);

    nrep(i, 1, ans.size()) {
        a[ans[0]] += a[ans[i]];
        a[ans[i]] = 0;
        lol.emplace_back(1e9, ans[i] + 1, ans[0] + 1);
        ignore.insert(ans[i]);
    }

    int other = ans[0] == 0 ? 1 : 0;
    ignore.insert(other);

    rep(i, n) {
        if (ignore.count(i)) {
            continue;
        }

        lol.emplace_back(1e9, i + 1, other + 1);
        a[other] += a[i];
        a[i] = 0;
    }

    lol.emplace_back(a[other] / k, other + 1, ans[0] + 1);

    a[ans[0]] += a[other] / k * k;

    if (a[ans[0]] < v) {
        cout << "NO\n";
        return 0;
    }

    ll diff = a[ans[0]] - v;

    cout << "YES\n";
    lol.emplace_back(diff / k, ans[0] + 1, ans[0] == 0 ? 2 : 1);

    printans(lol);
}