Problem:
Score: 500 points

Problem Statement

Takahashi will take part in an eating contest. Teams of N members will compete in this contest, and Takahashi's team consists of N players numbered 1 through N from youngest to oldest. The consumption coefficient of Member i is A_i.

In the contest, N foods numbered 1 through N will be presented, and the difficulty of Food i is F_i. The details of the contest are as follows:

A team should assign one member to each food, and should not assign the same member to multiple foods.

It will take x \times y seconds for a member to finish the food, where x is the consumption coefficient of the member and y is the difficulty of the dish.

The score of a team is the longest time it takes for an individual member to finish the food.

Before the contest, Takahashi's team decided to do some training. In one set of training, a member can reduce his/her consumption coefficient by 1, as long as it does not go below 0. However, for financial reasons, the N members can do at most K sets of training in total.

What is the minimum possible score of the team, achieved by choosing the amounts of members' training and allocating the dishes optimally?

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

0 \leq K \leq 10^{18}

1 \leq A_i \leq 10^6\ (1 \leq i \leq N)

1 \leq F_i \leq 10^6\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N
F_1 F_2 ... F_N

Output

Print the minimum possible score of the team.

Sample Input 1

3 5
4 2 1
2 3 1

Sample Output 1

2

They can achieve the score of 2, as follows:

Member 1 does 4 sets of training and eats Food 2 in (4-4) \times 3 = 0 seconds.

Member 2 does 1 set of training and eats Food 3 in (2-1) \times 1 = 1 second.

Member 3 does 0 sets of training and eats Food 1 in (1-0) \times 2 = 2 seconds.

They cannot achieve a score of less than 2, so the answer is 2.

Sample Input 2

3 8
4 2 1
2 3 1

Sample Output 2

0

They can choose not to do exactly K sets of training.

Sample Input 3

11 14
3 1 4 1 5 9 2 6 5 3 5
8 9 7 9 3 2 3 8 4 6 2

Sample Output 3

12

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
namespace Program
{
    public static class ABC144E
    {
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var K = NN;
            var AList = NNList(N);
            var FList = NNList(N);
            var sortedA = AList.OrderByRand().OrderBy(e => e).ToList();
            var sortedF = FList.OrderByRand().OrderBy(e => e).ToList();
            var left = -1L;
            var right = 0L;
            for (var i = 0; i < N; i++) right += sortedA[i] * sortedF[i];
            while (right - left > 1)
            {
                var mid = (right - left) / 2 + left;
                var kCount = 0L;
                for (var i = 0; i < N; i++)
                {
                    var a = sortedA[i];
                    var f = sortedF[i];
                    kCount += a - mid / f;
                }
                if (kCount <= K)
                {
                    right = mid;
                }
                else
                {
                    left = mid;
                }
            }
            Console.WriteLine(right);

        }
        static public void Main(string[] args) { if (args.Length == 0) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); } var t = new Thread(Solve, 134217728); t.Start(); t.Join(); Console.Out.Flush(); }
        static class Console_
        {
            static Queue<string> param = new Queue<string>();
            public static string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        }
        static long NN => long.Parse(Console_.NextString());
        static double ND => double.Parse(Console_.NextString());
        static string NS => Console_.NextString();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => xorshift);
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IEnumerable<long> Primes(long x) { if (x < 2) yield break; yield return 2; var halfx = x / 2; var table = new bool[halfx + 1]; var max = (long)(Math.Sqrt(x) / 2); for (long i = 1; i <= max; ++i) { if (table[i]) continue; var add = 2 * i + 1; yield return add; for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true; } for (long i = max + 1; i <= halfx; ++i) if (!table[i] && 2 * i + 1 <= x) yield return 2 * i + 1; }
        static IEnumerable<long> Factors(long x) { if (x < 2) yield break; while (x % 2 == 0) { x /= 2; yield return 2; } var max = (long)Math.Sqrt(x); for (long i = 3; i <= max; i += 2) while (x % i == 0) { x /= i; yield return i; } if (x != 1) yield return x; }
        static IEnumerable<long> Divisor(long x) { if (x < 1) yield break; var max = (long)Math.Sqrt(x); for (long i = 1; i <= max; ++i) { if (x % i != 0) continue; yield return i; if (i != x / i) yield return x / i; } }
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
        static long GCD(long a, long b) { while (b > 0) { var tmp = b; b = a % b; a = tmp; } return a; }
        static long LCM(long a, long b) => a * b / GCD(a, b);
        static Mod Pow(Mod x, long y) { Mod a = 1; while (y != 0) { if ((y & 1) == 1) a.Mul(x); x.Mul(x); y >>= 1; } return a; }
        static long Pow(long x, long y) { long a = 1; while (y != 0) { if ((y & 1) == 1) a *= x; x *= x; y >>= 1; } return a; }
        static List<long> _fact = new List<long>() { 1 };
        static void _B(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); }
        static long Comb(long n, long k) { _B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; }
        static long Perm(long n, long k) { _B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)]; }
        static Func<TR> Lambda<TR>(Func<Func<TR>, TR> f) { Func<TR> t = () => default(TR); return t = () => f(t); }
        static Func<T1, TR> Lambda<T1, TR>(Func<T1, Func<T1, TR>, TR> f) { Func<T1, TR> t = x1 => default(TR); return t = x1 => f(x1, t); }
        static Func<T1, T2, TR> Lambda<T1, T2, TR>(Func<T1, T2, Func<T1, T2, TR>, TR> f) { Func<T1, T2, TR> t = (x1, x2) => default(TR); return t = (x1, x2) => f(x1, x2, t); }
        static Func<T1, T2, T3, TR> Lambda<T1, T2, T3, TR>(Func<T1, T2, T3, Func<T1, T2, T3, TR>, TR> f) { Func<T1, T2, T3, TR> t = (x1, x2, x3) => default(TR); return t = (x1, x2, x3) => f(x1, x2, x3, t); }
        static Func<T1, T2, T3, T4, TR> Lambda<T1, T2, T3, T4, TR>(Func<T1, T2, T3, T4, Func<T1, T2, T3, T4, TR>, TR> f) { Func<T1, T2, T3, T4, TR> t = (x1, x2, x3, x4) => default(TR); return t = (x1, x2, x3, x4) => f(x1, x2, x3, x4, t); }
        static List<T> LCS<T>(T[] s, T[] t) where T : IEquatable<T> { int sl = s.Length, tl = t.Length; var dp = new int[sl + 1, tl + 1]; for (var i = 0; i < sl; i++) for (var j = 0; j < tl; j++) dp[i + 1, j + 1] = s[i].Equals(t[j]) ? dp[i, j] + 1 : Max(dp[i + 1, j], dp[i, j + 1]); { var r = new List<T>(); int i = sl, j = tl; while (i > 0 && j > 0) if (s[--i].Equals(t[--j])) r.Add(s[i]); else if (dp[i, j + 1] > dp[i + 1, j]) ++j; else ++i; r.Reverse(); return r; } }
        static long LIS<T>(T[] array, bool strict) { var l = new List<T>(); foreach (var e in array) { var i = l.BinarySearch(e); if (i < 0) i = ~i; else if (!strict) ++i; if (i == l.Count) l.Add(e); else l[i] = e; } return l.Count; }
        class PQ<T>
        {
            List<T> h; Comparison<T> c; public T Peek => h[0]; public int Count => h.Count;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, Comparer<T>.Default.Compare, asc) { }
            public PQ(bool asc = true) : this(Comparer<T>.Default.Compare, asc) { }
            public void Push(T v) { var i = h.Count; h.Add(v); while (i > 0) { var ni = (i - 1) / 2; if (c(v, h[ni]) >= 0) break; h[i] = h[ni]; i = ni; } h[i] = v; }
            public T Pop() { var r = h[0]; var v = h[h.Count - 1]; h.RemoveAt(h.Count - 1); if (h.Count == 0) return r; var i = 0; while (i * 2 + 1 < h.Count) { var i1 = i * 2 + 1; var i2 = i * 2 + 2; if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2; if (c(v, h[i1]) <= 0) break; h[i] = h[i1]; i = i1; } h[i] = v; return r; }
        }
        class PQ<TK, TV>
        {
            PQ<Tuple<TK, TV>> q; public Tuple<TK, TV> Peek => q.Peek; public int Count => q.Count;
            public PQ(int cap, Comparison<TK> c, bool asc = true) { q = new PQ<Tuple<TK, TV>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TK> c, bool asc = true) { q = new PQ<Tuple<TK, TV>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, Comparer<TK>.Default.Compare, asc) { }
            public PQ(bool asc = true) : this(Comparer<TK>.Default.Compare, asc) { }
            public void Push(TK k, TV v) => q.Push(Tuple.Create(k, v));
            public Tuple<TK, TV> Pop() => q.Pop();
        }
        public class UF
        {
            long[] d;
            public UF(long s) { d = Repeat(-1L, s).ToArray(); }
            public bool Unite(long x, long y) { x = Root(x); y = Root(y); if (x != y) { if (d[y] < d[x]) { var t = y; y = x; x = t; } d[x] += d[y]; d[y] = x; } return x != y; }
            public bool IsSame(long x, long y) => Root(x) == Root(y);
            public long Root(long x) => d[x] < 0 ? x : d[x] = Root(d[x]);
            public long Count(long x) => -d[Root(x)];
        }
        struct Mod : IEquatable<Mod>, IEquatable<long>
        {
            static public long _mod = 1000000007; long v;
            public Mod(long x) { if (x < _mod && x >= 0) v = x; else if ((v = x % _mod) < 0) v += _mod; }
            static public implicit operator Mod(long x) => new Mod(x);
            static public implicit operator long(Mod x) => x.v;
            public void Add(Mod x) { if ((v += x.v) >= _mod) v -= _mod; }
            public void Sub(Mod x) { if ((v -= x.v) < 0) v += _mod; }
            public void Mul(Mod x) => v = (v * x.v) % _mod;
            public void Div(Mod x) => v = (v * Inverse(x.v)) % _mod;
            static public Mod operator +(Mod x, Mod y) { var t = x.v + y.v; return t >= _mod ? new Mod { v = t - _mod } : new Mod { v = t }; }
            static public Mod operator -(Mod x, Mod y) { var t = x.v - y.v; return t < 0 ? new Mod { v = t + _mod } : new Mod { v = t }; }
            static public Mod operator *(Mod x, Mod y) => x.v * y.v;
            static public Mod operator /(Mod x, Mod y) => x.v * Inverse(y.v);
            static public bool operator ==(Mod x, Mod y) => x.v == y.v;
            static public bool operator !=(Mod x, Mod y) => x.v != y.v;
            static public long Inverse(long x) { long b = _mod, r = 1, u = 0, t = 0; while (b > 0) { var q = x / b; t = u; u = r - q * u; r = t; t = b; b = x - q * b; x = t; } return r < 0 ? r + _mod : r; }
            public bool Equals(Mod x) => v == x.v;
            public bool Equals(long x) => v == x;
            public override bool Equals(object x) => x == null ? false : Equals((Mod)x);
            public override int GetHashCode() => v.GetHashCode();
            public override string ToString() => v.ToString();
            static List<Mod> _fact = new List<Mod>() { 1 };
            static void B(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); }
            static public Mod Comb(long n, long k) { B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; }
            static public Mod Perm(long n, long k) { B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)]; }
        }
        class Tree
        {
            long N; int l; List<long>[] p; int[] d; long[][] pr; long r; Tuple<long, long, int>[] e; Tuple<long, long>[] b; bool lca; bool euler; bool bfs;
            public Tree(List<long>[] p_, long r_) { N = p_.Length; p = p_; r = r_; lca = false; euler = false; }
            public Tuple<long, long>[] BFSRoot() { if (!bfs) { var nb = new List<Tuple<long, long>>(); var q = new Queue<long>(); var d = new bool[N]; nb.Add(Tuple.Create(r, -1L)); d[r] = true; q.Enqueue(r); while (q.Count > 0) { var w = q.Dequeue(); foreach (var i in p[w]) { if (d[i]) continue; d[i] = true; q.Enqueue(i); nb.Add(Tuple.Create(i, w)); } } b = nb.ToArray(); bfs = true; } return b; }
            public Tuple<long, long>[] BFSLeaf() => BFSRoot().Reverse().ToArray();
            public Tuple<long, long, int>[] Euler() { if (!euler) { var ne = new List<Tuple<long, long, int>>(); var s = new Stack<Tuple<long, long>>(); var d = new bool[N]; d[r] = true; s.Push(Tuple.Create(r, -1L)); while (s.Count > 0) { var w = s.Peek(); var ad = true; foreach (var i in p[w.Item1]) { if (d[i]) continue; d[i] = true; ad = false; s.Push(Tuple.Create(i, w.Item1)); } if (!ad || p[w.Item1].Count == 1) ne.Add(Tuple.Create(w.Item1, w.Item2, 1)); if (ad) { s.Pop(); ne.Add(Tuple.Create(w.Item1, w.Item2, -1)); } } e = ne.ToArray(); euler = true; } return e; }
            public long LCA(long u, long v) { if (!lca) { l = 0; while (N > (1 << l)) l++; d = new int[N]; pr = Repeat(0, l).Select(_ => new long[N]).ToArray(); d[r] = 0; pr[0][r] = -1; var q = new Stack<long>(); q.Push(r); while (q.Count > 0) { var w = q.Pop(); foreach (var i in p[w]) { if (i == pr[0][w]) continue; q.Push(i); d[i] = d[w] + 1; pr[0][i] = w; } } for (var k = 0; k + 1 < l; k++) for (var w = 0; w < N; w++) if (pr[k][w] < 0) pr[k + 1][w] = -1; else pr[k + 1][w] = pr[k][pr[k][w]]; lca = true; } if (d[u] > d[v]) { var t = u; u = v; v = t; } for (var k = 0; k < l; k++) if ((((d[v] - d[u]) >> k) & 1) != 0) v = pr[k][v]; if (u == v) return u; for (var k = l - 1; k >= 0; k--) if (pr[k][u] != pr[k][v]) { u = pr[k][u]; v = pr[k][v]; } return pr[0][u]; }
        }
        class BT<T> where T : IComparable
        {
            class Node { public Node l; public Node r; public T v; public bool b; public int c; }
            Comparison<T> c; Node r; bool ch; T lm;
            public BT(Comparison<T> _c) { c = _c; }
            public BT() : this((x, y) => x.CompareTo(y)) { }
            bool R(Node n) => n != null && !n.b;
            bool B(Node n) => n != null && n.b;
            long C(Node n) => n?.c ?? 0;
            Node RtL(Node n) { Node m = n.r, t = m.l; m.l = n; n.r = t; n.c -= m.c - (t?.c ?? 0); m.c += n.c - (t?.c ?? 0); return m; }
            Node RtR(Node n) { Node m = n.l, t = m.r; m.r = n; n.l = t; n.c -= m.c - (t?.c ?? 0); m.c += n.c - (t?.c ?? 0); return m; }
            Node RtLR(Node n) { n.l = RtL(n.l); return RtR(n); }
            Node RtRL(Node n) { n.r = RtR(n.r); return RtL(n); }
            public void Add(T x) { r = A(r, x); r.b = true; }
            Node A(Node n, T x) { if (n == null) { ch = true; return new Node() { v = x, c = 1 }; } if (c(x, n.v) < 0) n.l = A(n.l, x); else n.r = A(n.r, x); n.c++; return Bl(n); }
            Node Bl(Node n) { if (!ch) return n; if (!B(n)) return n; if (R(n.l) && R(n.l.l)) { n = RtR(n); n.l.b = true; } else if (R(n.l) && R(n.l.r)) { n = RtLR(n); n.l.b = true; } else if (R(n.r) && R(n.r.l)) { n = RtRL(n); n.r.b = true; } else if (R(n.r) && R(n.r.r)) { n = RtL(n); n.r.b = true; } else ch = false; return n; }
            public void Remove(T x) { r = Rm(r, x); if (r != null) r.b = true; }
            Node Rm(Node n, T x) { if (n == null) { ch = false; return n; } n.c--; var r = c(x, n.v); if (r < 0) { n.l = Rm(n.l, x); return BlL(n); } if (r > 0) { n.r = Rm(n.r, x); return BlR(n); } if (n.l == null) { ch = n.b; return n.r; } n.l = RmM(n.l); n.v = lm; return BlL(n); }
            Node RmM(Node n) { n.c--; if (n.r != null) { n.r = RmM(n.r); return BlR(n); } lm = n.v; ch = n.b; return n.l; }
            Node BlL(Node n) { if (!ch) return n; if (B(n.r) && R(n.r.l)) { var b = n.b; n = RtRL(n); n.b = b; n.l.b = true; ch = false; } else if (B(n.r) && R(n.r.r)) { var b = n.b; n = RtL(n); n.b = b; n.r.b = true; n.l.b = true; ch = false; } else if (B(n.r)) { ch = n.b; n.b = true; n.r.b = false; } else { n = RtL(n); n.b = true; n.l.b = false; n.l = BlL(n.l); ch = false; } return n; }
            Node BlR(Node n) { if (!ch) return n; if (B(n.l) && R(n.l.r)) { var b = n.b; n = RtLR(n); n.b = b; n.r.b = true; ch = false; } else if (B(n.l) && R(n.l.l)) { var b = n.b; n = RtR(n); n.b = b; n.l.b = true; n.r.b = true; ch = false; } else if (B(n.l)) { ch = n.b; n.b = true; n.l.b = false; } else { n = RtR(n); n.b = true; n.r.b = false; n.r = BlR(n.r); ch = false; } return n; }
            public T this[long i] { get { return At(r, i); } }
            T At(Node n, long i) { if (n == null) return default(T); if (n.l == null) if (i == 0) return n.v; else return At(n.r, i - 1); if (n.l.c == i) return n.v; if (n.l.c > i) return At(n.l, i); return At(n.r, i - n.l.c - 1); }
            public bool Have(T x) { var t = FindUpper(x); return t < C(r) && c(At(r, t), x) == 0; }
            public long FindUpper(T x, bool allowSame = true) => allowSame ? FL(r, x) + 1 : FU(r, x);
            long FU(Node n, T x) { if (n == null) return 0; var r = c(x, n.v); if (r < 0) return FU(n.l, x); return C(n.l) + 1 + FU(n.r, x); }
            public long FindLower(T x, bool allowSame = true) { var t = FL(r, x); if (allowSame) return t + 1 < C(r) && c(At(r, t + 1), x) == 0 ? t + 1 : t < 0 ? C(r) : t; return t < 0 ? C(r) : t; }
            long FL(Node n, T x) { if (n == null) return -1; var r = c(x, n.v); if (r > 0) return C(n.l) + 1 + FL(n.r, x); return FL(n.l, x); }
            public T Min() { Node n = r, p = null; while (n != null) { p = n; n = n.l; } return p == null ? default(T) : p.v; }
            public T Max() { Node n = r, p = null; while (n != null) { p = n; n = n.r; } return p == null ? default(T) : p.v; }
            public bool Any() => r != null;
            public long Count() => C(r);
            public IEnumerable<T> List() => L(r);
            IEnumerable<T> L(Node n) { if (n == null) yield break; foreach (var i in L(n.l)) yield return i; yield return n.v; foreach (var i in L(n.r)) yield return i; }
        }
        class Dict<K, V> : Dictionary<K, V>
        {
            Func<K, V> d;
            public Dict(Func<K, V> _d) { d = _d; }
            public Dict() : this(_ => default(V)) { }
            new public V this[K i] { get { V v; return TryGetValue(i, out v) ? v : base[i] = d(i); } set { base[i] = value; } }
            public override int GetHashCode() { var ret = 0; for (var e = GetEnumerator(); e.MoveNext();) { ret ^= e.Current.Key.GetHashCode(); ret ^= e.Current.Value.GetHashCode(); } return ret; }
            public override bool Equals(object obj) { var o = (Dict<K, V>)obj; foreach (var kv in o) { if (!ContainsKey(kv.Key) || !this[kv.Key].Equals(kv.Value)) return false; } return o.Count == Count; }
        }
        class Deque<T>
        {
            T[] b; int o, c;
            public int Count;
            public T this[int i] { get { return b[gi(i)]; } set { b[gi(i)] = value; } }
            public Deque(int cap = 16) { b = new T[c = cap]; }
            int gi(int i) { if (i >= c) throw new Exception(); var r = o + i; return r >= c ? r - c : r; }
            public void PushFront(T x) { if (Count == c) e(); if (--o < 0) o += b.Length; b[o] = x; ++Count; }
            public T PopFront() { if (Count-- == 0) throw new Exception(); var r = b[o++]; if (o >= c) o -= c; return r; }
            public T Front => b[o];
            public void PushBack(T x) { if (Count == c) e(); var i = o + Count++; b[i >= c ? i - c : i] = x; }
            public T PopBack() { if (Count == 0) throw new Exception(); return b[gi(--Count)]; }
            public T Back => b[gi(Count - 1)];
            void e() { T[] nb = new T[c << 1]; if (o > c - Count) { var l = b.Length - o; Array.Copy(b, o, nb, 0, l); Array.Copy(b, 0, nb, l, Count - l); } else Array.Copy(b, o, nb, 0, Count); b = nb; o = 0; c <<= 1; }
            public void Insert(int i, T x) { if (i > Count) throw new Exception(); this.PushFront(x); for (int j = 0; j < i; j++) this[j] = this[j + 1]; this[i] = x; }
            public T RemoveAt(int i) { if (i < 0 || i >= Count) throw new Exception(); var r = this[i]; for (int j = i; j > 0; j--) this[j] = this[j - 1]; this.PopFront(); return r; }
        }
        class SegTree<T>
        {
            int n; T ti; Func<T, T, T> f; T[] dat;
            public SegTree(long _n, T _ti, Func<T, T, T> _f) { n = 1; while (n < _n) n <<= 1; ti = _ti; f = _f; dat = Repeat(ti, n << 1).ToArray(); for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public SegTree(List<T> l, T _ti, Func<T, T, T> _f) : this(l.Count, _ti, _f) { for (var i = 0; i < l.Count; i++) dat[n + i] = l[i]; for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public void Update(long i, T v) { dat[i += n] = v; while ((i >>= 1) > 0) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public T Query(long l, long r) { var vl = ti; var vr = ti; for (long li = n + l, ri = n + r; li < ri; li >>= 1, ri >>= 1) { if ((li & 1) == 1) vl = f(vl, dat[li++]); if ((ri & 1) == 1) vr = f(dat[--ri], vr); } return f(vl, vr); }
            public T this[long idx] { get { return dat[idx + n]; } set { Update(idx, value); } }
        }
        class LazySegTree<T, E>
        {
            int n, height; T ti; E ei; Func<T, T, T> f; Func<T, E, T> g; Func<E, E, E> h; T[] dat; E[] laz;
            public LazySegTree(long _n, T _ti, E _ei, Func<T, T, T> _f, Func<T, E, T> _g, Func<E, E, E> _h) { n = 1; height = 0; while (n < _n) { n <<= 1; ++height; } ti = _ti; ei = _ei; f = _f; g = _g; h = _h; dat = Repeat(ti, n << 1).ToArray(); laz = Repeat(ei, n << 1).ToArray(); for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public LazySegTree(List<T> l, T _ti, E _ei, Func<T, T, T> _f, Func<T, E, T> _g, Func<E, E, E> _h) : this(l.Count, _ti, _ei, _f, _g, _h) { for (var i = 0; i < l.Count; i++) dat[n + i] = l[i]; for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            T Reflect(long i) => laz[i].Equals(ei) ? dat[i] : g(dat[i], laz[i]);
            void Eval(long i) { if (laz[i].Equals(ei)) return; laz[(i << 1) | 0] = h(laz[(i << 1) | 0], laz[i]); laz[(i << 1) | 1] = h(laz[(i << 1) | 1], laz[i]); dat[i] = Reflect(i); laz[i] = ei; }
            void Thrust(long i) { for (var j = height; j > 0; j--) Eval(i >> j); }
            void Recalc(long i) { while ((i >>= 1) > 0) dat[i] = f(Reflect((i << 1) | 0), Reflect((i << 1) | 1)); }
            public void Update(long l, long r, E v) { Thrust(l += n); Thrust(r += n - 1); for (long li = l, ri = r + 1; li < ri; li >>= 1, ri >>= 1) { if ((li & 1) == 1) { laz[li] = h(laz[li], v); ++li; } if ((ri & 1) == 1) { --ri; laz[ri] = h(laz[ri], v); } } Recalc(l); Recalc(r); }
            public T Query(long l, long r) { Thrust(l += n); Thrust(r += n - 1); var vl = ti; var vr = ti; for (long li = l, ri = r + 1; li < ri; li >>= 1, ri >>= 1) { if ((li & 1) == 1) vl = f(vl, Reflect(li++)); if ((ri & 1) == 1) vr = f(Reflect(--ri), vr); } return f(vl, vr); }
            public T this[long idx] { get { Thrust(idx += n); return dat[idx] = Reflect(idx); } set { Thrust(idx += n); dat[idx] = value; laz[idx] = ei; Recalc(idx); } }
        }
        class SlidingWindowAggregation<T>
        {
            T[][] l; T[][] a; int[] n; Func<T, T, T> f;
            public SlidingWindowAggregation(IEnumerable<T> ary, Func<T, T, T> _f) { l = new T[2][]; a = new T[2][]; n = new int[2]; f = _f; l[0] = new T[16]; a[0] = new T[16]; n[0] = 0; if (ary.Any()) { var t = ary.ToArray(); n[1] = t.Length; l[1] = new T[n[1]]; a[1] = new T[n[1]]; for (var i = 0; i < l[1].Length; i++) { l[1][i] = t[i]; if (i == 0) a[1][i] = t[i]; else a[1][i] = this.f(a[1][i - 1], t[i]); } } else { l[1] = new T[16]; a[1] = new T[16]; n[1] = 0; } }
            public SlidingWindowAggregation(Func<T, T, T> f) : this(new T[0], f) { }
            public int Count => n[0] + n[1];
            void Push(int la, T v) { if (l[la].Length == n[la]) { var nar = new T[n[la] * 2]; var nag = new T[n[la] * 2]; Array.Copy(l[la], nar, n[la]); Array.Copy(a[la], nag, n[la]); l[la] = nar; a[la] = nag; } if (n[la] == 0) a[la][0] = v; else a[la][n[la]] = la == 0 ? f(v, a[la][n[la] - 1]) : f(a[la][n[la] - 1], v); l[la][n[la]++] = v; }
            public void PushBack(T val) => Push(1, val);
            public void PushFront(T val) => Push(0, val);
            public T Pop(int la) { var lb = 1 - la; if (n[la] == 0) { if (n[lb] == 0) throw new Exception(); var m = (n[lb] - 1) / 2; if (l[la].Length <= m) { l[la] = new T[m + 1]; a[la] = new T[m + 1]; } n[la] = 0; for (var i = m; i >= 0; i--) { if (n[la] == 0) a[la][n[la]] = l[lb][i]; else a[la][n[la]] = la == 0 ? f(l[lb][i], a[la][n[la] - 1]) : f(a[la][n[la] - 1], l[lb][i]); l[la][n[la]++] = l[lb][i]; } for (var i = m + 1; i < n[lb]; i++) { var j = i - m - 1; if (j == 0) a[lb][j] = l[lb][i]; else a[lb][j] = la == 0 ? f(l[lb][i], a[lb][j - 1]) : f(a[lb][j - 1], l[lb][i]); l[lb][j] = l[lb][i]; } n[lb] -= n[la]; } return l[la][--n[la]]; }
            public T PopBack() => Pop(1);
            public T PopFront() => Pop(0);
            public T Aggregate() { if (n[0] == 0 && n[1] == 0) throw new Exception(); else if (n[1] == 0) return a[0][n[0] - 1]; else if (n[0] == 0) return a[1][n[1] - 1]; else return f(a[0][n[0] - 1], a[1][n[1] - 1]); }
        }
    }
}