LUXURY 7

A.Little Pony and Expected Maximum

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 454C

Description

Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.

The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability . Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.

Input

A single line contains two integers m and n (1 ≤ m, n ≤ 10⁵).

Output

Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn‘t exceed 10 ^- 4.

Sample Input

Input

6 1

Output

3.500000000000

Input

6 3

Output

4.958333333333

Input

2 2

Output

1.750000000000

Hint

Consider the third test example. If you‘ve made two tosses:

1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.

The probability of each outcome is 0.25, that is expectation equals to:

You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value

:抛6面骰子3次，如果要计算最大值为3的情况：3^3 - (3-1)^3

注意到很容易就能让指数爆long long，所以变成（3/6)^3 - ((3-1)/6)^3 。利用排列组合原理。

B。

Pashmak and Graph

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 459E

Description

Pashmak‘s homework is a problem about graphs. Although he always tries to do his homework completely, he can‘t solve this problem. As you know, he‘s really weak at graph theory; so try to help him in solving the problem.

You are given a weighted directed graph with n vertices and m edges. You need to find a path (perhaps, non-simple) with maximum number of edges, such that the weights of the edges increase along the path. In other words, each edge of the path must have strictly greater weight than the previous edge in the path.

Help Pashmak, print the number of edges in the required path.

Input

The first line contains two integers n, m(2 ≤ n ≤ 3·10⁵; 1 ≤ m ≤ min(n·(n - 1), 3·10⁵)). Then, m lines follows. The i-th line contains three space separated integers: u_i, v_i, w_i(1 ≤ u_i, v_i ≤ n; 1 ≤ w_i ≤ 10⁵) which indicates that there‘s a directed edge with weight w_i from vertex u_i to vertex v_i.

It‘s guaranteed that the graph doesn‘t contain self-loops and multiple edges.

Output

Print a single integer — the answer to the problem.

Sample Input

Input

3 31 2 12 3 13 1 1

Output

1

Input

3 31 2 12 3 23 1 3

Output

3

Input

6 71 2 13 2 52 4 22 5 22 6 95 4 34 3 4

Output

6

Hint

In the first sample the maximum trail can be any of this trails: .

In the second sample the maximum trail is .

In the third sample the maximum trail is .

一到很水的dp，只要知道原理，学过背包的都能做出来。

C - Boredom

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 456C

Description

Alex doesn‘t like boredom. That‘s why whenever he gets bored, he comes up with games. One long winter evening he came up with a game and decided to play it.

Given a sequence a consisting of n integers. The player can make several steps. In a single step he can choose an element of the sequence (let‘s denote it a_k) and delete it, at that all elements equal to a_k + 1 and a_k - 1 also must be deleted from the sequence. That step bringsa_k points to the player.

Alex is a perfectionist, so he decided to get as many points as possible. Help him.

Input

The first line contains integer n (1 ≤ n ≤ 10⁵) that shows how many numbers are in Alex‘s sequence.

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁵).

Output

Print a single integer — the maximum number of points that Alex can earn.

Sample Input

Input

21 2

Output

2

Input

31 2 3

Output

4

Input

91 2 1 3 2 2 2 2 3

Output

10

Hint

Consider the third test example. At first step we need to choose any element equal to 2. After that step our sequence looks like this [2, 2, 2, 2]. Then we do 4 steps, on each step we choose any element equals to 2. In total we earn 10 points.

dp题，很水。

D - Pashmak and Parmida‘s problem

Time Limit:3000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 459D

Description

Parmida is a clever girl and she wants to participate in Olympiads this year. Of course she wants her partner to be clever too (although he‘s not)! Parmida has prepared the following test problem for Pashmak.

There is a sequence a that consists of n integers a₁, a₂, ..., a_n. Let‘s denote f(l, r, x) the number of indices k such that: l ≤ k ≤ r anda_k = x. His task is to calculate the number of pairs of indicies i, j(1 ≤ i < j ≤ n) such that f(1, i, a_i) > f(j, n, a_j).

Help Pashmak with the test.

Input

The first line of the input contains an integer n(1 ≤ n ≤ 10⁶). The second line contains n space-separated integers a₁, a₂, ..., a_n(1 ≤ a_i ≤ 10⁹).

Output

Print a single integer — the answer to the problem.

Sample Input

Input

71 2 1 1 2 2 1

Output

8

Input

31 1 1

Output

1

Input

51 2 3 4 5

Output

0

树状数组，F[i]表示 < i 的f（l，r，x）有多少个。

E - Present

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 460C

Description

Little beaver is a beginner programmer, so informatics is his favorite subject. Soon his informatics teacher is going to have a birthday and the beaver has decided to prepare a present for her. He planted n flowers in a row on his windowsill and started waiting for them to grow. However, after some time the beaver noticed that the flowers stopped growing. The beaver thinks it is bad manners to present little flowers. So he decided to come up with some solutions.

There are m days left to the birthday. The height of the i-th flower (assume that the flowers in the row are numbered from 1 to n from left to right) is equal to a_i at the moment. At each of the remaining m days the beaver can take a special watering and water w contiguous flowers (he can do that only once at a day). At that each watered flower grows by one height unit on that day. The beaver wants the height of the smallest flower be as large as possible in the end. What maximum height of the smallest flower can he get?

Input

The first line contains space-separated integers n, m and w(1 ≤ w ≤ n ≤ 10⁵; 1 ≤ m ≤ 10⁵). The second line contains space-separated integers a₁, a₂, ..., a_n(1 ≤ a_i ≤ 10⁹).

Output

Print a single integer — the maximum final height of the smallest flower.

Sample Input

Input

6 2 32 2 2 2 1 1

Output

2

Input

2 5 15 8

Output

9

Hint

In the first sample beaver can water the last 3 flowers at the first day. On the next day he may not to water flowers at all. In the end he will get the following heights: [2, 2, 2, 3, 2, 2]. The smallest flower has height equal to 2. It‘s impossible to get height 3 in this test.

二分，并用pre[l] += 1 , pre[l+w] -= 1 ,来维护区间的变化，使判断的过程用O（n）实现。

但用线段树的成段更新也能过。