#1198106 (C++23) No.2078 魔抜けなパープル

• 問題: No.2078 魔抜けなパープル
• ユーザー: drken1215
• 提出日時: 2026-11-11 13:00:34
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 108 ms / 2,000 ms
• コード長: 24,165 bytes
• コンパイル時間: 3,258 ms
• コンパイル使用メモリ: 366,084 KB
• 実行使用メモリ: 9,812 KB
• 最終ジャッジ日時: 2026-11-11 13:00:41
• 合計ジャッジ時間: 5,454 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge4_0

ファイルパターン	結果
sample	AC * 1
other	AC * 7

ソースコード

#line 1 "test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2078"

#include <bits/stdc++.h>
using namespace std;

#line 4 "https://drken1215.github.io/algorithm/template.hpp.html"
using namespace std;

// My library is in https://github.com/drken1215/algorithm
#line 4 "https://drken1215.github.io/algorithm/Others/macro.hpp.html"
using namespace std;

using ll = long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
using tll = array<long long, 3>;
using fll = array<long long, 4>;
using vint = vector<int>;
using vll = vector<long long>;
using dint = deque<int>;
using dll = deque<long long>;
using vvint = vector<vector<int>>;
using vvll = vector<vector<long long>>;
using vpll = vector<pair<long long, long long>>;
template<class T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;

template<class S, class T> inline bool chmax(S &a, T b) { return (a < b ? a = b, 1 : 0); }
template<class S, class T> inline bool chmin(S &a, T b) { return (a > b ? a = b, 1 : 0); }
template<class S, class T> inline auto maxll(S a, T b) { return max(ll(a), ll(b)); }
template<class S, class T> inline auto minll(S a, T b) { return min(ll(a), ll(b)); }
template<class T> auto max(const T &a) { return *max_element(a.begin(), a.end()); }
template<class T> auto min(const T &a) { return *min_element(a.begin(), a.end()); }
template<class T> auto argmax(const T &a) { return max_element(a.begin(), a.end()) - a.begin(); }
template<class T> auto argmin(const T &a) { return min_element(a.begin(), a.end()) - a.begin(); }
template<class T> auto accum(const vector<T> &a) { return accumulate(a.begin(), a.end(), T()); }
template<class T> auto accum(const deque<T> &a) { return accumulate(a.begin(), a.end(), T()); }

#define REP(i, a) for (long long i = 0; i < (long long)(a); i++)
#define REP2(i, a, b) for (long long i = a; i < (long long)(b); i++)
#define RREP(i, a) for (long long i = (a)-1; i >= (long long)(0); --i)
#define RREP2(i, a, b) for (long long i = (b)-1; i >= (long long)(a); --i)
#define EB emplace_back
#define PF push_front
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define ALL(x) x.begin(), x.end()
#line 3 "https://drken1215.github.io/algorithm/Others/stl_container_stream.hpp.html"
using namespace std;

// input stream
template<class T> istream& operator >> (istream &is, vector<T> &P)
{ for (int i = 0; i < (int)P.size(); ++i) cin >> P[i]; return is; }
template<class T> istream& operator >> (istream &is, deque<T> &P)
{ for (int i = 0; i < (int)P.size(); ++i) cin >> P[i]; return is; }
template<class T> istream& operator >> (istream &is, vector<vector<T>> &P)
{ for (int i = 0; i < (int)P.size(); ++i) cin >> P[i]; return is; }

// output stream
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
template<class S, class T> ostream& operator << (ostream &s, const pair<S, T> &P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 2> &P)
{ return s << '<' << P[0] << "," << P[1] << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 3> &P)
{ return s << '<' << P[0] << "," << P[1] << "," << P[2] << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 4> &P)
{ return s << '<' << P[0] << "," << P[1] << "," << P[2] << "," << P[3] << '>'; }
template<class T> ostream& operator << (ostream &s, const vector<string> &P)
{ for (int i = 0; i < P.size(); ++i) { s << P[i] << endl; } return s; }
template<class T> ostream& operator << (ostream &s, const vector<T> &P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, const deque<T> &P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, const vector<vector<T>> &P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, const set<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, const multiset<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, const unordered_set<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class S, class T> ostream& operator << (ostream &s, const map<S, T> &P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
template<class S, class T> ostream& operator << (ostream &s, const unordered_map<S, T> &P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }

// Yes/No
void yes(bool a) { cout << (a ? "yes" : "no") << endl; }
void YES(bool a) { cout << (a ? "YES" : "NO") << endl; }
void Yes(bool a) { cout << (a ? "Yes" : "No") << endl; }
#line 4 "https://drken1215.github.io/algorithm/Optimization/monge_shortest_path.hpp.html"
using namespace std;

#line 4 "https://drken1215.github.io/algorithm/Optimization/simple_larsch.hpp.html"
using namespace std;

// noshi's simplified LARSCH
// find shortest path from vertex 0 on DAG in O(N log N)
// vertex: 0, 1, 2, ..., N
// f(i, j) must be Monge (Then, A(j, i) = dp[i] + f(i, j) is also Monge)
// slide access OK
template<class VAL> struct SimpleLARSCH {
    VAL INF = numeric_limits<VAL>::max() / 2;
    int CNT_INF = numeric_limits<int>::max() / 2;

    // results
    vector<VAL> dp;
    vector<int> cnt, prev;

    // solver (random access ver)
    template<class FUNC> vector<pair<VAL, int>> solve(int N, const FUNC &f, bool minimize_cnt = true) {
        dp.assign(N + 1, INF);
        cnt.assign(N + 1, CNT_INF);
        prev.assign(N + 1, 0);
        dp[0] = 0, cnt[0] = 0;

        auto relax = [&](int l, int r) -> void {
            VAL val = dp[l] + f(l, r);
            int cn = cnt[l] + 1;
            if (dp[r] > val || (dp[r] == val && (minimize_cnt ? cn < cnt[r] : cn > cnt[r]))) {
                dp[r] = val;
                cnt[r] = cn;
                prev[r] = l;
            }
        };
        auto rec = [&](auto &&rec, int l, int r) -> void {
            if (r - l <= 1) return;
            int m = (l + r) / 2;
            for (int k = prev[l]; k <= prev[r]; k++) relax(k, m);
            rec(rec, l, m);
            for (int k = l + 1; k <= m; k++) relax(k, r);
            rec(rec, m, r);
        };

        if (N > 0) relax(0, N), rec(rec, 0, N);
        vector<pair<VAL, int>> res(N + 1, make_pair(numeric_limits<VAL>::max() / 2, -1));
        res[0].first = VAL(0);
        for (int i = 1; i <= N; i++) res[i] = {dp[i], prev[i]};
        return res;
    }

    // solver (slide access ver)
    template<class STATE, class ADD, class DEL, class GETCOST> vector<pair<VAL, int>> solve
    (int N, const STATE &ini, const ADD &add, const DEL &del, const GETCOST &get, bool minimize_cnt = true) {
        dp.assign(N + 1, INF);
        cnt.assign(N + 1, CNT_INF);
        prev.assign(N + 1, 0);
        dp[0] = 0, cnt[0] = 0;

        STATE win[2] = { ini, ini };
        int cl[2] = {0, 0}, cr[2] = {0, 0};

        auto move_cursor = [&](int c, int l, int r) {
            while (cr[c] < r) add(win[c], cr[c]++);
            while (cl[c] > l) add(win[c], --cl[c]);
            while (cr[c] > r) del(win[c], --cr[c]);
            while (cl[c] < l) del(win[c], cl[c]++);
        };
        auto relax = [&](int c, int l, int r) {
            move_cursor(c, l, r);
            VAL val = dp[l] + get(win[c]);
            int cn = cnt[l] + 1;
            if (dp[r] > val || (dp[r] == val && (minimize_cnt ? cn < cnt[r] : cn > cnt[r]))) {
                dp[r] = val;
                cnt[r] = cn;
                prev[r] = l;
            }
        };
        auto rec = [&](auto &&rec, int l, int r) -> void {
            if (r - l <= 1) return;
            int m = (l + r) / 2;
            for (int k = prev[l]; k <= prev[r]; k++) relax(0, k, m);
            rec(rec, l, m);
            for (int k = l + 1; k <= m; k++) relax(1, k, r);
            rec(rec, m, r);
        };

        if (N > 0) relax(0, 0, N), rec(rec, 0, N);
        vector<pair<VAL, int>> res(N + 1, make_pair(numeric_limits<VAL>::max() / 2, -1));
        res[0].first = VAL(0);
        for (int i = 1; i <= N; i++) res[i] = {dp[i], prev[i]};
        return res;
    }

    // reconstruct the shortest path
    vector<int> reconstruct() {
        int N = (int)dp.size() - 1;
        vector<int> path;
        for (int v = N; v > 0; v = prev[v]) path.emplace_back(v);
        path.emplace_back(0);
        reverse(path.begin(), path.end());
        return path;
    }
};
#line 4 "https://drken1215.github.io/algorithm/Optimization/larsch.hpp.html"
using namespace std;

// LARSCH, in O(N)
// vertex: 0, 1, 2, ..., N
// f(i, j) must be Monge (Then, A(j, i) = dp[i] + f(i, j) is also Monge)
template<class VAL, class FUNC> struct SubLARSCH {
    struct RowReduce;
    struct ColReduce;
    struct ColMap {
        const ColMap* parent = nullptr;
        const vector<int> *v = nullptr;
        constexpr int mapping(int i) const {
            int x = (v ? (*v)[i] : i);
            return (parent ? parent->mapping(x) : x);
        }
    };
    struct Eval {
        const FUNC *f = nullptr;
        long long a = 1, b = 0;  // row = a * i + b
        const ColMap *cm = nullptr;
        constexpr VAL operator () (int i, int j) const {
            int i2 = int(a * i + b), j2 = (cm ? cm -> mapping(j) : j);
            return (*f)(i2, j2);
        }
    };
    struct RowReduce {
        int N;
        Eval e;
        int cur_row = 0, state = 0;
        unique_ptr<ColReduce> rec;
        constexpr RowReduce(int N_, const Eval &e_) : N(N_), e(e_) {
            int M = N / 2;
            if (M > 0) {
                Eval e2 = e;
                e2.a = e.a * 2, e2.b = e.a + e.b;
                rec = make_unique<ColReduce>(M, e2);
            }
        }
        constexpr void reset() {
            cur_row = 0, state = 0;
            if (rec) rec->reset();
        }
        int get_argmin() {
            int i = cur_row++;
            if (!(i & 1)) {
                int prev = state, next = (i + 1 == N ? N - 1 : rec->get_argmin());
                state = next;
                int res = prev;
                for (int j = prev + 1; j <= next; j++) {
                    if (e(i, res) > e(i, j)) res = j;
                }
                return res;
            } else {
                return (e(i, state) <= e(i, i) ? state : i);
            }
        }
    };
    struct ColReduce {
        int N;
        Eval e;
        int cur_row = 0;
        vector<int> cols;
        ColMap cm;
        RowReduce rec;
        constexpr ColReduce(int N_, const Eval &e_) 
        : N(N_), e(e_), cols(), cm{e.cm, &cols}, rec(N_, Eval{e.f, e.a, e.b, &cm}) {
            cols.reserve(N);
        } 
        constexpr void reset() {
            cur_row = 0;
            cols.clear();
            rec.reset();
        }
        constexpr void push_col(int i, int j) {
            while (!cols.empty()) {
                int siz = (int)cols.size();
                if (siz == i) break;
                int last = cols.back();
                if (e(siz - 1, last) > e(siz - 1, j)) cols.pop_back();
                else break;
            }
            if ((int)cols.size() != N) cols.emplace_back(j);
        }
        constexpr int get_argmin() {
            int i = cur_row++;
            if (i == 0) {
                cols.clear();
                cols.emplace_back(0);
            } else {
                push_col(i, i * 2 - 1);
                push_col(i, i * 2);
            }
            return cols[rec.get_argmin()];
        }
    };

    FUNC f;
    ColMap root_cm;
    Eval root_eval;
    unique_ptr<RowReduce> base;
    explicit SubLARSCH(int N_, const FUNC &f_) 
    : f(std::move(f_)), root_cm{nullptr, nullptr}, root_eval{&f, 1, 0, &root_cm} {
        base = make_unique<RowReduce>(N_, root_eval);
    }
    constexpr void reset() {
        base->reset();
    }
    constexpr int get_argmin() {
        return base->get_argmin();
    }
};

template<class VAL> struct LARSCH {
    VAL INF = numeric_limits<VAL>::max() / 2;
    int CNT_INF = numeric_limits<int>::max() / 2;

    // results
    vector<VAL> dp;
    vector<int> cnt, prev;

    // solver
    template<class FUNC> vector<pair<VAL, int>> solve(int N, const FUNC &f) {
        dp.assign(N + 1, INF);
        cnt.assign(N + 1, CNT_INF);
        prev.assign(N + 1, 0);
        vector<pair<VAL, int>> res(N + 1, make_pair(numeric_limits<VAL>::max() / 2, -1));
        dp[0] = 0, cnt[0] = 0, res[0].first = 0;
        auto f2 = [&](int i, int j) -> VAL {
            i++;
            if (i <= j) return INF;
            else return dp[j] + f(j, i);
        };
        SubLARSCH<VAL, decltype(f2)> lar(N, f2);
        for (int r = 1; r <= N; r++) {
            int l = lar.get_argmin();
            dp[r] = dp[l] + f(l, r);
            prev[r] = l;
            cnt[r] = cnt[l] + 1;
        }
        for (int r = 1; r <= N; r++) res[r] = {dp[r], prev[r]};
        return res;
    }

    // reconstruct the shortest path
    vector<int> reconstruct() {
        int N = (int)dp.size() - 1;
        vector<int> path;
        for (int v = N; v > 0; v = prev[v]) path.emplace_back(v);
        path.emplace_back(0);
        reverse(path.begin(), path.end());
        return path;
    }
};
#line 4 "https://drken1215.github.io/algorithm/Optimization/dd_monotone_minima.hpp.html"
using namespace std;

#line 4 "https://drken1215.github.io/algorithm/Optimization/monotone_minima.hpp.html"
using namespace std;

// find min_j f(i, j) for all i, by Monotone Minima, O(H + W log H)
// f(i, j) must be monotone (argmin is not decreasing)
// slide access OK
template<class VAL, class FUNC> void MonotoneMinimaRec
(int HL, int HR, int WL, int WR, const FUNC &f, vector<pair<VAL, int>> &res) {
    if (HR - HL <= 0) return;
    int HM = (HL + HR) / 2;
    res[HM].second = WL;
    for (int i = WL; i < WR; i++) {
        VAL val = f(HM, i);
        if (res[HM].first > val) res[HM] = make_pair(val, i);
    }
    MonotoneMinimaRec(HL, HM, WL, res[HM].second + 1, f, res);
    MonotoneMinimaRec(HM + 1, HR, res[HM].second, WR, f, res);
}
template<class VAL, class FUNC> vector<pair<VAL, int>> MonotoneMinima(int H, int W, const FUNC &f) {
    vector<pair<VAL, int>> res(H, make_pair(numeric_limits<VAL>::max() / 2, -1));
    MonotoneMinimaRec(0, H, 0, W, f, res);
    return res;
}
#line 7 "https://drken1215.github.io/algorithm/Optimization/dd_monotone_minima.hpp.html"

// find shortest path on DAG by D&D Monotone Minima, O(N (log N)^2)
// vertex: 0, 1, 2, ..., N
// A(j, i) = dp[i] + f(i, j) must be monotone (argmin is not decreasing)
// Attention: Even if f is monotone, A is not necessarily monotone
// slide access OK
template<class VAL> struct DDMonotoneMinima {
    VAL INF = numeric_limits<VAL>::max() / 2;
    int CNT_INF = numeric_limits<int>::max() / 2;

    // results
    vector<VAL> dp;
    vector<int> cnt, prev;

    // solver (random access ver)
    template<class FUNC> vector<pair<VAL, int>> solve(int N, const FUNC &f) {
        dp.assign(N + 1, INF);
        cnt.assign(N + 1, CNT_INF);
        prev.assign(N + 1, 0);
        dp[0] = 0, cnt[0] = 0;
        vector<pair<VAL, int>> res(N + 1, make_pair(INF, -1));
        vector<pair<VAL, int>> tmp(N + 1, make_pair(INF, -1));
        res[0].first = VAL(0);
        auto f2 = [&](int i, int j) -> VAL { return res[j].first + f(j, i); };
        auto rec = [&](auto &&rec, int left, int right) -> void {
            if (right - left <= 1) return;
            int mid = (left + right) / 2;
            rec(rec, left, mid);
            for (int i = mid; i < right; i++) tmp[i] = {INF, -1};
            MonotoneMinimaRec(mid, right, left, mid, f2, tmp);
            for (int i = mid; i < right; i++) if (tmp[i].first < res[i].first) res[i] = tmp[i];
            rec(rec, mid, right);
        };
        rec(rec, 0, N + 1);
        for (int r = 1; r <= N; r++) {
            dp[r] = res[r].first;
            prev[r] = res[r].second;
            if (prev[r] != -1) cnt[r] = cnt[prev[r]] + 1;
        }
        return res;
    }

    // solver (slide access ver)
    template<class ADD, class DEL, class GETCOST> vector<pair<VAL, int>> solve
    (int N, const ADD &add, const DEL &del, const GETCOST &get) {
        int left = 0, right = 0;
        auto f = [&](int i, int j) -> long long {
            while (left < i) del(left++);
            while (i < left) add(--left);
            while (right < j) add(right++);
            while (j < right) del(--right);
            return get();
        };
        auto f2 = [&](int i, int j) -> VAL { return (j < i ? dp[j] + f(j, i) : INF); };
        return solve(N, f2);
    }

    // reconstruct the shortest path
    vector<int> reconstruct() {
        int N = (int)dp.size() - 1;
        vector<int> path;
        for (int v = N; v > 0; v = prev[v]) path.emplace_back(v);
        path.emplace_back(0);
        reverse(path.begin(), path.end());
        return path;
    }
};
#line 4 "https://drken1215.github.io/algorithm/Optimization/dd_smawk.hpp.html"
using namespace std;

#line 4 "https://drken1215.github.io/algorithm/Optimization/smawk.hpp.html"
using namespace std;

// find min_j f(i, j) for all i, by SMAWK, O(H + W)
// f(i, j) must be totally monotone
// slide access NG
template<class VAL, class FUNC> void SMAWKRec
(const vector<int> &X, const vector<int> &Y, const FUNC &f, vector<pair<VAL, int>> &res) {
    if (X.empty()) return;

    // Reduce Step
    vector<int> X2, Y2;
    for (auto y : Y) {
        while (!Y2.empty()) {
            int py = Y2.back(), x = X[(int)Y2.size() - 1];
            if (f(x, y) >= f(x, py)) break;
            Y2.pop_back();
        }
        if (Y2.size() < X.size()) Y2.emplace_back(y);
    }

    // Recurse Step
    for (int i = 1; i < (int)X.size(); i += 2) X2.emplace_back(X[i]);
    SMAWKRec(X2, Y2, f, res);

    // Interpolate Step
    int p = 0;
    for (int i = 0; i < (int)X.size(); i += 2) {
        int lim = (i + 1 < (int)X.size() ? res[X[i + 1]].second : Y.back()), best = Y[p];
        while (Y[p] < lim) {
            p++;
            if (f(X[i], Y[p]) < f(X[i], best)) best = Y[p];
        }
        res[X[i]] = {f(X[i], best), best};
    }
}
template<class VAL, class FUNC> vector<pair<VAL, int>> SMAWK(int H, int W, const FUNC &f) {
    if (H == 0) return {};
    assert(W > 0);
    vector<pair<VAL, int>> res(H, make_pair(numeric_limits<VAL>::max() / 2, -1));
    vector<int> X(H), Y(W);
    for (int i = 0; i < H; i++) X[i] = i;
    for (int j = 0; j < W; j++) Y[j] = j;
    SMAWKRec(X, Y, f, res);
    return res;
}
#line 7 "https://drken1215.github.io/algorithm/Optimization/dd_smawk.hpp.html"

// find shortest path on DAG by D&D SMAWK, O(N log N)
// vertex: 0, 1, 2, ..., N
// A(j, i) = dp[i] + f(i, j) must be totally monotone
// Attention: Even if f is totally monotone, A is not necessarily totally monotone
// slide access NG
template<class VAL> struct DDSMAWK {
    VAL INF = numeric_limits<VAL>::max() / 2;
    int CNT_INF = numeric_limits<int>::max() / 2;

    // results
    vector<VAL> dp;
    vector<int> cnt, prev;

    // solver
    template<class FUNC> vector<pair<VAL, int>> solve(int N, const FUNC &f) {
        dp.assign(N + 1, INF);
        cnt.assign(N + 1, CNT_INF);
        prev.assign(N + 1, 0);
        vector<pair<VAL, int>> res(N + 1, make_pair(numeric_limits<VAL>::max() / 2, -1));
        vector<pair<VAL, int>> tmp(N + 1);
        dp[0] = 0, cnt[0] = 0, res[0].first = VAL(0);
        auto f2 = [&](int i, int j) -> VAL { return res[j].first + f(j, i); };
        auto rec = [&](auto &&rec, int left, int right) -> void {
            if (right - left <= 1) return;
            int mid = (left + right) / 2;
            vector<int> X(right - mid), Y(mid - left);
            for (int i = mid; i < right; i++) X[i - mid] = i;
            for (int j = left; j < mid; j++) Y[j - left] = j;
            rec(rec, left, mid);
            SMAWKRec(X, Y, f2, tmp);
            for (auto x : X) if (tmp[x].first < res[x].first) res[x] = tmp[x];
            rec(rec, mid, right);
        };
        rec(rec, 0, N + 1);
        for (int r = 1; r <= N; r++) {
            dp[r] = res[r].first;
            prev[r] = res[r].second;
            if (prev[r] != -1) cnt[r] = cnt[prev[r]] + 1;
        }
        return res;
    }

    // reconstruct the shortest path
    vector<int> reconstruct() {
        int N = (int)dp.size() - 1;
        vector<int> path;
        for (int v = N; v > 0; v = prev[v]) path.emplace_back(v);
        path.emplace_back(0);
        reverse(path.begin(), path.end());
        return path;
    }
};
#line 10 "https://drken1215.github.io/algorithm/Optimization/monge_shortest_path.hpp.html"

// Monge Shortest Path Wrapper
// vertex: 0, 1, 2, ..., N
// f(i, j) must be Monge (Then, A(j, i) = dp[i] + f(i, j) is also Monge)
template<class VAL> struct MongeShortestPath {
    VAL INF = numeric_limits<VAL>::max() / 2;
    int CNT_INF = numeric_limits<int>::max() / 2;

    // results
    vector<VAL> dp;
    vector<int> cnt, prev;

    // solver (random access ver)
    template<class FUNC> vector<pair<VAL, int>> solve(int N, const FUNC &f
    , const string solver = "simple_larsch") {
        vector<pair<VAL, int>> res(N + 1, make_pair(numeric_limits<VAL>::max() / 2, -1));
        if (solver == "simple_larsch") {
            SimpleLARSCH<VAL> opt;
            res = opt.solve(N, f);
            dp = opt.dp, cnt = opt.cnt, prev = opt.prev;
        } else if (solver == "larsch") {
            LARSCH<VAL> opt;
            res = opt.solve(N, f);
            dp = opt.dp, cnt = opt.cnt, prev = opt.prev;
        } else if (solver == "monotone") {
            DDMonotoneMinima<VAL> opt;
            res = opt.solve(N, f);
            dp = opt.dp, cnt = opt.cnt, prev = opt.prev;
        } else if (solver == "smawk") {
            DDSMAWK<VAL> opt;
            res = opt.solve(N, f);
            dp = opt.dp, cnt = opt.cnt, prev = opt.prev;
        } else {
            cout << "no solver" << endl;
            assert(true);
        }
        return res;
    }

    // solver (slide access ver)
    template<class STATE, class ADD, class DEL, class GETCOST> vector<pair<VAL, int>> solve
    (int N, const STATE &ini, const ADD &add, const DEL &del, const GETCOST &get, const string solver = "simple_larsch") {
        vector<pair<VAL, int>> res;
        if (solver == "simple_larsch") {
            SimpleLARSCH<VAL> opt;
            res = opt.solve(N, ini, add, del, get);
            dp = opt.dp, cnt = opt.cnt, prev = opt.prev;
        } else if (solver == "monotone") {
            DDMonotoneMinima<VAL> opt;
            STATE st = ini;
            int left = 0, right = 0;
            auto f = [&](int i, int j) -> long long {
                while (left < i) del(st, left++);
                while (i < left) add(st, --left);
                while (right < j) add(st, right++);
                while (j < right) del(st, --right);
                return get(st);
            };
            res = opt.solve(N, f);
            dp = opt.dp, cnt = opt.cnt, prev = opt.prev;
        }else {
            cout << "no solver" << endl;
            assert(true);
        }
        return res;
    }

    // reconstruct the shortest path
    vector<int> reconstruct() {
        int N = (int)dp.size() - 1;
        vector<int> path;
        for (int v = N; v > 0; v = prev[v]) path.emplace_back(v);
        path.emplace_back(0);
        reverse(path.begin(), path.end());
        return path;
    }
};
#line 8 "test.cpp"

/*
    dp[j] = min_{j < i} (dp[i] + func(i, j))
    func(i, j) = (j - i)^2 + X
*/
void solve() {
    ll X, A;
    cin >> X >> A;
    auto func = [&](ll i, ll j) -> ll { return (j - i) * (j - i) + X; };
    MongeShortestPath<ll> opt;
    auto res = opt.solve(A, func);
    cout << res.back().first << endl;
}

int main() {
    int T;
    cin >> T;
    while (T--) solve();
}