You are given two arrays A and B consisting of integers, sorted in non-decreasing order. Check whether it is possible to choose k numbers in array A and choose m numbers in array B so that any number chosen in the first array is strictly less than any number chosen in the second array.
The first line contains two integers nA, nB (1 ≤ nA, nB ≤ 105), separated by a space — the sizes of arrays A and B, correspondingly.
The second line contains two integers k and m (1 ≤ k ≤ nA, 1 ≤ m ≤ nB), separated by a space.
The third line contains nA numbers a1, a2, ... anA ( - 109 ≤ a1 ≤ a2 ≤ ... ≤ anA ≤ 109), separated by spaces — elements of array A.
The fourth line contains nB integers b1, b2, ... bnB ( - 109 ≤ b1 ≤ b2 ≤ ... ≤ bnB ≤ 109), separated by spaces — elements of array B.
Print "YES" (without the quotes), if you can choose k numbers in array A and m numbers in array B so that any number chosen in array A was strictly less than any number chosen in array B. Otherwise, print "NO" (without the quotes).
3 3
2 1
1 2 3
3 4 5
YES
3 3
3 3
1 2 3
3 4 5
NO
5 2
3 1
1 1 1 1 1
2 2
YES
In the first sample test you can, for example, choose numbers 1 and 2 from array A and number 3 from array B (1 < 3 and 2 < 3).
In the second sample test the only way to choose k elements in the first array and m elements in the second one is to choose all numbers in both arrays, but then not all the numbers chosen in A will be less than all the numbers chosen in B: 
.
In this task you need to process a set of stock exchange orders and use them to create order book.
An order is an instruction of some participant to buy or sell stocks on stock exchange. The order number i has price pi, direction di — buy or sell, and integer qi. This means that the participant is ready to buy or sell qi stocks at price pi for one stock. A value qi is also known as a volume of an order.
All orders with the same price p and direction d are merged into one aggregated order with price p and direction d. The volume of such order is a sum of volumes of the initial orders.
An order book is a list of aggregated orders, the first part of which contains sell orders sorted by price in descending order, the second contains buy orders also sorted by price in descending order.
An order book of depth s contains s best aggregated orders for each direction. A buy order is better if it has higher price and a sell order is better if it has lower price. If there are less than s aggregated orders for some direction then all of them will be in the final order book.
You are given n stock exhange orders. Your task is to print order book of depth s for these orders.
The input starts with two positive integers n and s (1 ≤ n ≤ 1000, 1 ≤ s ≤ 50), the number of orders and the book depth.
Next n lines contains a letter di (either 'B' or 'S'), an integer pi (0 ≤ pi ≤ 105) and an integer qi (1 ≤ qi ≤ 104) — direction, price and volume respectively. The letter 'B' means buy, 'S' means sell. The price of any sell order is higher than the price of any buy order.
Print no more than 2s lines with aggregated orders from order book of depth s. The output format for orders should be the same as in input.
6 2
B 10 3
S 50 2
S 40 1
S 50 6
B 20 4
B 25 10
S 50 8
S 40 1
B 25 10
B 20 4
Denote (x, y) an order with price x and volume y. There are 3 aggregated buy orders (10, 3), (20, 4), (25, 10) and two sell orders (50, 8), (40, 1) in the sample.
You need to print no more than two best orders for each direction, so you shouldn't print the order (10 3) having the worst price among buy orders.
You are given three sticks with positive integer lengths of a, b, and c centimeters. You can increase length of some of them by some positive integer number of centimeters (different sticks can be increased by a different length), but in total by at most l centimeters. In particular, it is allowed not to increase the length of any stick.
Determine the number of ways to increase the lengths of some sticks so that you can form from them a non-degenerate (that is, having a positive area) triangle. Two ways are considered different, if the length of some stick is increased by different number of centimeters in them.
The single line contains 4 integers a, b, c, l (1 ≤ a, b, c ≤ 3·105, 0 ≤ l ≤ 3·105).
Print a single integer — the number of ways to increase the sizes of the sticks by the total of at most l centimeters, so that you can make a non-degenerate triangle from it.
1 1 1 2
4
1 2 3 1
2
10 2 1 7
0
In the first sample test you can either not increase any stick or increase any two sticks by 1 centimeter.
In the second sample test you can increase either the first or the second stick by one centimeter. Note that the triangle made from the initial sticks is degenerate and thus, doesn't meet the conditions.
You've got array A, consisting of n integers and a positive integer k. Array A is indexed by integers from 1 to n.
You need to permute the array elements so that value
The first line contains two integers n, k (2 ≤ n ≤ 3·105, 1 ≤ k ≤ min(5000, n - 1)).
The second line contains n integers A[1], A[2], ..., A[n] ( - 109 ≤ A[i] ≤ 109), separate by spaces — elements of the array A.
Print the minimum possible value of the sum described in the statement.
3 2
1 2 4
1
5 2
3 -5 3 -5 3
0
6 3
4 3 4 3 2 5
3
In the first test one of the optimal permutations is 1 4 2.
In the second test the initial order is optimal.
In the third test one of the optimal permutations is 2 3 4 4 3 5.
'In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of clauses, where a clause is a disjunction of literals' (cited from https://en.wikipedia.org/wiki/Conjunctive_normal_form)
In the other words, CNF is a formula of type 
, where & represents a logical "AND" (conjunction), 
represents a logical "OR" (disjunction), and vij are some boolean variables or their negations. Each statement in brackets is called a clause, and vij are called literals.
You are given a CNF containing variables x1, ..., xm and their negations. We know that each variable occurs in at most two clauses (with negation and without negation in total). Your task is to determine whether this CNF is satisfiable, that is, whether there are such values of variables where the CNF value is true. If CNF is satisfiable, then you also need to determine the values of the variables at which the CNF is true.
It is guaranteed that each variable occurs at most once in each clause.
The first line contains integers n and m (1 ≤ n, m ≤ 2·105) — the number of clauses and the number variables, correspondingly.
Next n lines contain the descriptions of each clause. The i-th line first contains first number ki (ki ≥ 1) — the number of literals in the i-th clauses. Then follow space-separated literals vij (1 ≤ |vij| ≤ m). A literal that corresponds to vij is x|vij| either with negation, if vij is negative, or without negation otherwise.
If CNF is not satisfiable, print a single line "NO" (without the quotes), otherwise print two strings: string "YES" (without the quotes), and then a string of m numbers zero or one — the values of variables in satisfying assignment in the order from x1 to xm.
2 2
2 1 -2
2 2 -1
YES
11
4 3
1 1
1 2
3 -1 -2 3
1 -3
NO
5 6
2 1 2
3 1 -2 3
4 -3 5 4 6
2 -6 -4
1 5
YES
100010
In the first sample test formula is 
. One of possible answer is x1 = TRUE, x2 = TRUE.