meetforever/GRPO_CL huggingface dataset:
user: Nian is a monster which lives deep in the oceans. Once a year, it shows up on the land, devouring livestock and even people. In order to keep the monster away, people fill their villages with red colour, light, and cracking noise, all of which frighten the monster out of coming.

Little Tommy has n lanterns and Big Banban has m lanterns. Tommy's lanterns have brightness a_1, a_2, ..., a_{n}, and Banban's have brightness b_1, b_2, ..., b_{m} respectively.

Tommy intends to hide one of his lanterns, then Banban picks one of Tommy's non-hidden lanterns and one of his own lanterns to form a pair. The pair's brightness will be the product of the brightness of two lanterns.

Tommy wants to make the product as small as possible, while Banban tries to make it as large as possible.

You are asked to find the brightness of the chosen pair if both of them choose optimally.


-----Input-----

The first line contains two space-separated integers n and m (2 ≤ n, m ≤ 50).

The second line contains n space-separated integers a_1, a_2, ..., a_{n}.

The third line contains m space-separated integers b_1, b_2, ..., b_{m}.

All the integers range from  - 10^9 to 10^9.


-----Output-----

Print a single integer — the brightness of the chosen pair.


-----Examples-----
Input
2 2
20 18
2 14

Output
252

Input
5 3
-1 0 1 2 3
-1 0 1

Output
2



-----Note-----

In the first example, Tommy will hide 20 and Banban will choose 18 from Tommy and 14 from himself.

In the second example, Tommy will hide 3 and Banban will choose 2 from Tommy and 1 from himself.
user: A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:
 - In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.
For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.
You are given a positive integer K. Find the K-th smallest lunlun number.

-----Constraints-----
 - 1 \leq K \leq 10^5
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
K

-----Output-----
Print the answer.

-----Sample Input-----
15

-----Sample Output-----
23

We will list the 15 smallest lunlun numbers in ascending order:
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
21,
22,
23.

Thus, the answer is 23.
user: Given is a permutation P of \{1, 2, \ldots, N\}.
For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.
Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

-----Constraints-----
 -  2 \le N \le 10^5 
 -  1 \le P_i \le N 
 -  P_i \neq P_j  (i \neq j)
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
P_1 P_2 \ldots P_N

-----Output-----
Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

-----Sample Input-----
3
2 3 1

-----Sample Output-----
5

X_{1, 2} = 2, X_{1, 3} = 2, and X_{2, 3} = 1, so the sum is 2 + 2 + 1 = 5.
user: Given is an integer N.
Determine whether there is a pair of positive integers (A, B) such that 3^A + 5^B = N, and find one such pair if it exists.

-----Constraints-----
 - 1 \leq N \leq 10^{18}
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N

-----Output-----
If there is no pair (A, B) that satisfies the condition, print -1.
If there is such a pair, print A and B of one such pair with space in between. If there are multiple such pairs, any of them will be accepted.

-----Sample Input-----
106

-----Sample Output-----
4 2

We have 3^4 + 5^2 = 81 + 25 = 106, so (A, B) = (4, 2) satisfies the condition.
user: Caracal is fighting with a monster.
The health of the monster is H.
Caracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:
 - If the monster's health is 1, it drops to 0.
 - If the monster's health, X, is greater than 1, that monster disappears. Then, two new monsters appear, each with the health of \lfloor X/2 \rfloor.
(\lfloor r \rfloor denotes the greatest integer not exceeding r.)
Caracal wins when the healths of all existing monsters become 0 or below.
Find the minimum number of attacks Caracal needs to make before winning.

-----Constraints-----
 - 1 \leq H \leq 10^{12}
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
H

-----Output-----
Find the minimum number of attacks Caracal needs to make before winning.

-----Sample Input-----
2

-----Sample Output-----
3

When Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of 1.
Then, Caracal can attack each of these new monsters once and win with a total of three attacks.
user: Akari has n kinds of flowers, one of each kind.
She is going to choose one or more of these flowers to make a bouquet.
However, she hates two numbers a and b, so the number of flowers in the bouquet cannot be a or b.
How many different bouquets are there that Akari can make?
Find the count modulo (10^9 + 7).
Here, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq n \leq 10^9
 - 1 \leq a < b \leq \textrm{min}(n, 2 \times 10^5)

-----Input-----
Input is given from Standard Input in the following format:
n a b

-----Output-----
Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0.)

-----Sample Input-----
4 1 3

-----Sample Output-----
7

In this case, Akari can choose 2 or 4 flowers to make the bouquet.
There are 6 ways to choose 2 out of the 4 flowers, and 1 way to choose 4, so there are a total of 7 different bouquets that Akari can make.
user: Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.

-----Constraints-----
 - 1 \leq N < 10^{100}
 - 1 \leq K \leq 3

-----Input-----
Input is given from Standard Input in the following format:
N
K

-----Output-----
Print the count.

-----Sample Input-----
100
1

-----Sample Output-----
19

The following 19 integers satisfy the condition:
 - 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100
user: Tokitsukaze is one of the characters in the game "Kantai Collection". In this game, every character has a common attribute — health points, shortened to HP.

In general, different values of HP are grouped into $4$ categories:  Category $A$ if HP is in the form of $(4 n + 1)$, that is, when divided by $4$, the remainder is $1$;  Category $B$ if HP is in the form of $(4 n + 3)$, that is, when divided by $4$, the remainder is $3$;  Category $C$ if HP is in the form of $(4 n + 2)$, that is, when divided by $4$, the remainder is $2$;  Category $D$ if HP is in the form of $4 n$, that is, when divided by $4$, the remainder is $0$. 

The above-mentioned $n$ can be any integer.

These $4$ categories ordered from highest to lowest as $A > B > C > D$, which means category $A$ is the highest and category $D$ is the lowest.

While playing the game, players can increase the HP of the character. Now, Tokitsukaze wants you to increase her HP by at most $2$ (that is, either by $0$, $1$ or $2$). How much should she increase her HP so that it has the highest possible category?


-----Input-----

The only line contains a single integer $x$ ($30 \leq x \leq 100$) — the value Tokitsukaze's HP currently.


-----Output-----

Print an integer $a$ ($0 \leq a \leq 2$) and an uppercase letter $b$ ($b \in \lbrace A, B, C, D \rbrace$), representing that the best way is to increase her HP by $a$, and then the category becomes $b$.

Note that the output characters are case-sensitive.


-----Examples-----
Input
33

Output
0 A

Input
98

Output
1 B



-----Note-----

For the first example, the category of Tokitsukaze's HP is already $A$, so you don't need to enhance her ability.

For the second example:  If you don't increase her HP, its value is still $98$, which equals to $(4 \times 24 + 2)$, and its category is $C$.  If you increase her HP by $1$, its value becomes $99$, which equals to $(4 \times 24 + 3)$, and its category becomes $B$.  If you increase her HP by $2$, its value becomes $100$, which equals to $(4 \times 25)$, and its category becomes $D$. 

Therefore, the best way is to increase her HP by $1$ so that the category of her HP becomes $B$.
user: You have multiset of n strings of the same length, consisting of lowercase English letters. We will say that those strings are easy to remember if for each string there is some position i and some letter c of the English alphabet, such that this string is the only string in the multiset that has letter c in position i.

For example, a multiset of strings {"abc", "aba", "adc", "ada"} are not easy to remember. And multiset {"abc", "ada", "ssa"} is easy to remember because:   the first string is the only string that has character c in position 3;  the second string is the only string that has character d in position 2;  the third string is the only string that has character s in position 2. 

You want to change your multiset a little so that it is easy to remember. For a_{ij} coins, you can change character in the j-th position of the i-th string into any other lowercase letter of the English alphabet. Find what is the minimum sum you should pay in order to make the multiset of strings easy to remember.


-----Input-----

The first line contains two integers n, m (1 ≤ n, m ≤ 20) — the number of strings in the multiset and the length of the strings respectively. Next n lines contain the strings of the multiset, consisting only of lowercase English letters, each string's length is m.

Next n lines contain m integers each, the i-th of them contains integers a_{i}1, a_{i}2, ..., a_{im} (0 ≤ a_{ij} ≤ 10^6).


-----Output-----

Print a single number — the answer to the problem.


-----Examples-----
Input
4 5
abcde
abcde
abcde
abcde
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

Output
3

Input
4 3
abc
aba
adc
ada
10 10 10
10 1 10
10 10 10
10 1 10

Output
2

Input
3 3
abc
ada
ssa
1 1 1
1 1 1
1 1 1

Output
0
user: Bob is an active user of the social network Faithbug. On this network, people are able to engage in a mutual friendship. That is, if $a$ is a friend of $b$, then $b$ is also a friend of $a$. Each user thus has a non-negative amount of friends.

This morning, somebody anonymously sent Bob the following link: graph realization problem and Bob wants to know who that was. In order to do that, he first needs to know how the social network looks like. He investigated the profile of every other person on the network and noted down the number of his friends. However, he neglected to note down the number of his friends. Help him find out how many friends he has. Since there may be many possible answers, print all of them.


-----Input-----

The first line contains one integer $n$ ($1 \leq n \leq 5 \cdot 10^5$), the number of people on the network excluding Bob. 

The second line contains $n$ numbers $a_1,a_2, \dots, a_n$ ($0 \leq a_i \leq n$), with $a_i$ being the number of people that person $i$ is a friend of.


-----Output-----

Print all possible values of $a_{n+1}$ — the amount of people that Bob can be friend of, in increasing order.

If no solution exists, output $-1$.


-----Examples-----
Input
3
3 3 3

Output
3 

Input
4
1 1 1 1

Output
0 2 4 

Input
2
0 2

Output
-1

Input
35
21 26 18 4 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22

Output
13 15 17 19 21 



-----Note-----

In the first test case, the only solution is that everyone is friends with everyone. That is why Bob should have $3$ friends.

In the second test case, there are three possible solutions (apart from symmetries):   $a$ is friend of $b$, $c$ is friend of $d$, and Bob has no friends, or  $a$ is a friend of $b$ and both $c$ and $d$ are friends with Bob, or  Bob is friends of everyone. 

The third case is impossible to solve, as the second person needs to be a friend with everybody, but the first one is a complete stranger.
user: On her way to programming school tiger Dasha faced her first test — a huge staircase! [Image] 

The steps were numbered from one to infinity. As we know, tigers are very fond of all striped things, it is possible that it has something to do with their color. So on some interval of her way she calculated two values — the number of steps with even and odd numbers. 

You need to check whether there is an interval of steps from the l-th to the r-th (1 ≤ l ≤ r), for which values that Dasha has found are correct.


-----Input-----

In the only line you are given two integers a, b (0 ≤ a, b ≤ 100) — the number of even and odd steps, accordingly.


-----Output-----

In the only line print "YES", if the interval of steps described above exists, and "NO" otherwise.


-----Examples-----
Input
2 3

Output
YES

Input
3 1

Output
NO



-----Note-----

In the first example one of suitable intervals is from 1 to 5. The interval contains two even steps — 2 and 4, and three odd: 1, 3 and 5.
user: 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.


-----Input-----

The first line contains two integers n_{A}, n_{B} (1 ≤ n_{A}, n_{B} ≤ 10^5), separated by a space — the sizes of arrays A and B, correspondingly.

The second line contains two integers k and m (1 ≤ k ≤ n_{A}, 1 ≤ m ≤ n_{B}), separated by a space.

The third line contains n_{A} numbers a_1, a_2, ... a_{n}_{A} ( - 10^9 ≤ a_1 ≤ a_2 ≤ ... ≤ a_{n}_{A} ≤ 10^9), separated by spaces — elements of array A.

The fourth line contains n_{B} integers b_1, b_2, ... b_{n}_{B} ( - 10^9 ≤ b_1 ≤ b_2 ≤ ... ≤ b_{n}_{B} ≤ 10^9), separated by spaces — elements of array B.


-----Output-----

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).


-----Examples-----
Input
3 3
2 1
1 2 3
3 4 5

Output
YES

Input
3 3
3 3
1 2 3
3 4 5

Output
NO

Input
5 2
3 1
1 1 1 1 1
2 2

Output
YES



-----Note-----

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: $3 < 3$.
user: Petya is a beginner programmer. He has already mastered the basics of the C++ language and moved on to learning algorithms. The first algorithm he encountered was insertion sort. Petya has already written the code that implements this algorithm and sorts the given integer zero-indexed array a of size n in the non-decreasing order. for (int i = 1; i < n; i = i + 1)

{

   int j = i; 

   while (j > 0 && a[j] < a[j - 1])

   {

      swap(a[j], a[j - 1]); // swap elements a[j] and a[j - 1]

      j = j - 1;

   }

}



Petya uses this algorithm only for sorting of arrays that are permutations of numbers from 0 to n - 1. He has already chosen the permutation he wants to sort but he first decided to swap some two of its elements. Petya wants to choose these elements in such a way that the number of times the sorting executes function swap, was minimum. Help Petya find out the number of ways in which he can make the swap and fulfill this requirement.

It is guaranteed that it's always possible to swap two elements of the input permutation in such a way that the number of swap function calls decreases.


-----Input-----

The first line contains a single integer n (2 ≤ n ≤ 5000) — the length of the permutation. The second line contains n different integers from 0 to n - 1, inclusive — the actual permutation.


-----Output-----

Print two integers: the minimum number of times the swap function is executed and the number of such pairs (i, j) that swapping the elements of the input permutation with indexes i and j leads to the minimum number of the executions.


-----Examples-----
Input
5
4 0 3 1 2

Output
3 2

Input
5
1 2 3 4 0

Output
3 4



-----Note-----

In the first sample the appropriate pairs are (0, 3) and (0, 4). 

In the second sample the appropriate pairs are (0, 4), (1, 4), (2, 4) and (3, 4).
user: An array $b$ is called to be a subarray of $a$ if it forms a continuous subsequence of $a$, that is, if it is equal to $a_l$, $a_{l + 1}$, $\ldots$, $a_r$ for some $l, r$.

Suppose $m$ is some known constant. For any array, having $m$ or more elements, let's define it's beauty as the sum of $m$ largest elements of that array. For example:   For array $x = [4, 3, 1, 5, 2]$ and $m = 3$, the $3$ largest elements of $x$ are $5$, $4$ and $3$, so the beauty of $x$ is $5 + 4 + 3 = 12$.

 For array $x = [10, 10, 10]$ and $m = 2$, the beauty of $x$ is $10 + 10 = 20$.

You are given an array $a_1, a_2, \ldots, a_n$, the value of the said constant $m$ and an integer $k$. Your need to split the array $a$ into exactly $k$ subarrays such that:

  Each element from $a$ belongs to exactly one subarray.

 Each subarray has at least $m$ elements.

 The sum of all beauties of $k$ subarrays is maximum possible.


-----Input-----

The first line contains three integers $n$, $m$ and $k$ ($2 \le n \le 2 \cdot 10^5$, $1 \le m$, $2 \le k$, $m \cdot k \le n$) — the number of elements in $a$, the constant $m$ in the definition of beauty and the number of subarrays to split to.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^9 \le a_i \le 10^9$).


-----Output-----

In the first line, print the maximum possible sum of the beauties of the subarrays in the optimal partition.

In the second line, print $k-1$ integers $p_1, p_2, \ldots, p_{k-1}$ ($1 \le p_1 < p_2 < \ldots < p_{k-1} < n$) representing the partition of the array, in which:



 All elements with indices from $1$ to $p_1$ belong to the first subarray.

 All elements with indices from $p_1 + 1$ to $p_2$ belong to the second subarray.

 $\ldots$.

 All elements with indices from $p_{k-1} + 1$ to $n$ belong to the last, $k$-th subarray.

If there are several optimal partitions, print any of them.


-----Examples-----
Input
9 2 3
5 2 5 2 4 1 1 3 2

Output
21
3 5 
Input
6 1 4
4 1 3 2 2 3

Output
12
1 3 5 
Input
2 1 2
-1000000000 1000000000

Output
0
1 


-----Note-----

In the first example, one of the optimal partitions is $[5, 2, 5]$, $[2, 4]$, $[1, 1, 3, 2]$.

  The beauty of the subarray $[5, 2, 5]$ is $5 + 5 = 10$.  The beauty of the subarray $[2, 4]$ is $2 + 4 = 6$.  The beauty of the subarray $[1, 1, 3, 2]$ is $3 + 2 = 5$. 

The sum of their beauties is $10 + 6 + 5 = 21$.

In the second example, one optimal partition is $[4]$, $[1, 3]$, $[2, 2]$, $[3]$.
user: You are given an array $A$, consisting of $n$ positive integers $a_1, a_2, \dots, a_n$, and an array $B$, consisting of $m$ positive integers $b_1, b_2, \dots, b_m$. 

Choose some element $a$ of $A$ and some element $b$ of $B$ such that $a+b$ doesn't belong to $A$ and doesn't belong to $B$. 

For example, if $A = [2, 1, 7]$ and $B = [1, 3, 4]$, we can choose $1$ from $A$ and $4$ from $B$, as number $5 = 1 + 4$ doesn't belong to $A$ and doesn't belong to $B$. However, we can't choose $2$ from $A$ and $1$ from $B$, as $3 = 2 + 1$ belongs to $B$.

It can be shown that such a pair exists. If there are multiple answers, print any.

Choose and print any such two numbers.


-----Input-----

The first line contains one integer $n$ ($1\le n \le 100$) — the number of elements of $A$.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 200$) — the elements of $A$.

The third line contains one integer $m$ ($1\le m \le 100$) — the number of elements of $B$.

The fourth line contains $m$ different integers $b_1, b_2, \dots, b_m$ ($1 \le b_i \le 200$) — the elements of $B$.

It can be shown that the answer always exists.


-----Output-----

Output two numbers $a$ and $b$ such that $a$ belongs to $A$, $b$ belongs to $B$, but $a+b$ doesn't belong to nor $A$ neither $B$.

If there are multiple answers, print any.


-----Examples-----
Input
1
20
2
10 20

Output
20 20
Input
3
3 2 2
5
1 5 7 7 9

Output
3 1

Input
4
1 3 5 7
4
7 5 3 1

Output
1 1



-----Note-----

In the first example, we can choose $20$ from array $[20]$ and $20$ from array $[10, 20]$. Number $40 = 20 + 20$ doesn't belong to any of those arrays. However, it is possible to choose $10$ from the second array too.

In the second example, we can choose $3$ from array $[3, 2, 2]$ and $1$ from array $[1, 5, 7, 7, 9]$. Number $4 = 3 + 1$ doesn't belong to any of those arrays.

In the third example, we can choose $1$ from array $[1, 3, 5, 7]$ and $1$ from array $[7, 5, 3, 1]$. Number $2 = 1 + 1$ doesn't belong to any of those arrays.
user: There are n cities in Westeros. The i-th city is inhabited by a_{i} people. Daenerys and Stannis play the following game: in one single move, a player chooses a certain town and burns it to the ground. Thus all its residents, sadly, die. Stannis starts the game. The game ends when Westeros has exactly k cities left.

The prophecy says that if the total number of surviving residents is even, then Daenerys wins: Stannis gets beheaded, and Daenerys rises on the Iron Throne. If the total number of surviving residents is odd, Stannis wins and everything goes in the completely opposite way.

Lord Petyr Baelish wants to know which candidates to the throne he should support, and therefore he wonders, which one of them has a winning strategy. Answer to this question of Lord Baelish and maybe you will become the next Lord of Harrenholl.


-----Input-----

The first line contains two positive space-separated integers, n and k (1 ≤ k ≤ n ≤ 2·10^5) — the initial number of cities in Westeros and the number of cities at which the game ends. 

The second line contains n space-separated positive integers a_{i} (1 ≤ a_{i} ≤ 10^6), which represent the population of each city in Westeros.


-----Output-----

Print string "Daenerys" (without the quotes), if Daenerys wins and "Stannis" (without the quotes), if Stannis wins.


-----Examples-----
Input
3 1
1 2 1

Output
Stannis

Input
3 1
2 2 1

Output
Daenerys

Input
6 3
5 20 12 7 14 101

Output
Stannis



-----Note-----

In the first sample Stannis will use his move to burn a city with two people and Daenerys will be forced to burn a city with one resident. The only survivor city will have one resident left, that is, the total sum is odd, and thus Stannis wins.

In the second sample, if Stannis burns a city with two people, Daenerys burns the city with one resident, or vice versa. In any case, the last remaining city will be inhabited by two people, that is, the total sum is even, and hence Daenerys wins.