Problem Statement

You are given a length-N sequence of non-negative integers.
When B is a sequence obtained by choosing K elements from A and concatenating them without changing the order, find the maximum possible value of MEX(B).

Here, for a sequence X, we define MEX(X) as the unique non-negative integer m that satisfies the following conditions:

• Every integer i such that 0 \le i < m is contained in X.
• m is not contained in X.

Constraints

• All values in the input are integers.
• 1 \le K \le N \le 3 \times 10^5
• 0 \le A_i \le 10^9

Sample Input 1

7 3
2 0 2 3 2 1 9

Sample Output 1

3

In this input, A=(2,0,2,3,2,1,9), and you obtain the sequence B by picking K=3 elements. For example,

• If the 1-st, 2-nd, and 3-rd elements are chosen, MEX(B)=MEX(2,0,2)=1.
• If the 3-rd, 4-th, and 6-th elements are chosen, MEX(B)=MEX(2,3,1)=0.
• If the 2-nd, 6-th, and 7-th elements are chosen, MEX(B)=MEX(0,1,9)=2.
• If the 2-nd, 3-rd, and 6-th elements are chosen, MEX(B)=MEX(0,2,1)=3.

The maximum possible MEX is 3.

Problem Statement

Takahashi sent a string T consisting of lowercase English letters to Aoki. As a result, Aoki received a string T' consisting of lowercase English letters.

T' may have been altered from T. Specifically, exactly one of the following four conditions is known to hold.

• T' is equal to T.
• T' is a string obtained by inserting one lowercase English letter at one position (possibly the beginning and end) in T.
• T' is a string obtained by deleting one character from T.
• T' is a string obtained by changing one character in T to another lowercase English letter.

You are given the string T' received by Aoki and N strings S_1, S_2, \ldots, S_N consisting of lowercase English letters. Find all the strings among S_1, S_2, \ldots, S_N that could equal the string T sent by Takahashi.

Constraints

• N is an integer.
• 1 \leq N \leq 5 \times 10^5
• S_i and T' are strings of length between 1 and 5 \times 10^5, inclusive, consisting of lowercase English letters.
• The total length of S_1, S_2, \ldots, S_N is at most 5 \times 10^5.

Sample Input 1

5 ababc
ababc
babc
abacbc
abdbc
abbac

Sample Output 1

4
1 2 3 4

Among S_1, S_2, \ldots, S_5, the strings that could be equal to T are S_1, S_2, S_3, S_4, as explained below.

• S_1 could be equal to T, because T' = ababc is equal to S_1 = ababc.
• S_2 could be equal to T, because T' = ababc is obtained by inserting the letter a at the beginning of S_2 = babc.
• S_3 could be equal to T, because T' = ababc is obtained by deleting the fourth character c from S_3 = abacbc.
• S_4 could be equal to T, because T' = ababc is obtained by changing the third character d in S_4 = abdbc to b.
• S_5 could not be equal to T, because if we take S_5 = abbac as T, then T' = ababc does not satisfy any of the four conditions in the problem statement.

Sample Input 2

1 aoki
takahashi

Sample Output 2

0

Sample Input 3

9 atcoder
atoder
atcode
athqcoder
atcoder
tacoder
jttcoder
atoder
atceoder
atcoer

Sample Output 3

6
1 2 4 7 8 9

Problem Statement

Takahashi has decided to give one gift to Aoki and one gift to Snuke.
There are N candidates of gifts for Aoki, and their values are A_1, A_2, \ldots,A_N.
There are M candidates of gifts for Snuke, and their values are B_1, B_2, \ldots,B_M.

Takahashi wants to choose gifts so that the difference in values of the two gifts is at most D.

Determine if he can choose such a pair of gifts. If he can, print the maximum sum of values of the chosen gifts.

Constraints

• 1\leq N,M\leq 2\times 10^5
• 1\leq A_i,B_i\leq 10^{18}
• 0\leq D \leq 10^{18}
• All values in the input are integers.

Sample Input 1

2 3 2
3 10
2 5 15

Sample Output 1

8

The difference of values of the two gifts should be at most 2.
If he gives a gift with value 3 to Aoki and another with value 5 to Snuke, the condition is satisfied, achieving the maximum possible sum of values.
Thus, 3+5=8 should be printed.

Sample Input 2

3 3 0
1 3 3
6 2 7

Sample Output 2

-1

He cannot choose gifts to satisfy the condition. Note that the candidates of gifts for a person may contain multiple gifts with the same value.

Sample Input 3

1 1 1000000000000000000
1000000000000000000
1000000000000000000

Sample Output 3

2000000000000000000

Note that the answer may not fit into a 32-bit integer type.

Sample Input 4

8 6 1
2 5 6 5 2 1 7 9
7 2 5 5 2 4

Sample Output 4

14

Problem Statement

Takahashi has N pieces of chocolate. The i-th piece has a rectangular shape with a width of A_i centimeters and a length of B_i centimeters.
He also has M boxes. The i-th box has a rectangular shape with a width of C_i centimeters and a length of D_i centimeters.

Determine whether it is possible to put the N pieces of chocolate in the boxes under the conditions below.

• A box can contain at most one piece of chocolate.
• A_i \leq C_j and B_i \leq D_j must hold when putting the i-th piece of chocolate in the j-th box (they cannot be rotated).

Constraints

• 1 \leq N \leq M \leq 2\times 10^5
• 1 \leq A_i,B_i,C_i,D_i \leq 10^9
• All values in input are integers.

Sample Input 1

2 3
2 4
3 2
8 1 5
2 10 5

Sample Output 1

Yes

We can put the first piece of chocolate in the third box and the second piece in the first box.

Sample Input 2

2 2
1 1
2 2
100 1
100 1

Sample Output 2

No

A box can contain at most one piece of chocolate.

Sample Input 3

1 1
10
100
100
10

Sample Output 3

No

Sample Input 4

1 1
10
100
10
100

Sample Output 4

Yes

Problem Statement

You are given an integer N. Print a string S that satisfies all of the following conditions. If no such string exists, print -1.

• S is a string of length between 1 and 1000, inclusive, consisting of the characters 1, 2, 3, 4, 5, 6, 7, 8, 9, and * (multiplication symbol).
• S is a palindrome.
• The first character of S is a digit.
• The value of S when evaluated as a formula equals N.

Constraints

• 1 \leq N \leq 10^{12}
• N is an integer.

Sample Input 1

363

Sample Output 1

11*3*11

S = 11*3*11 satisfies the conditions in the problem statement. Another string that satisfies the conditions is S= 363.

Sample Input 2

101

Sample Output 2

-1

Note that S must not contain the digit 0.

Sample Input 3

3154625100

Sample Output 3

2*57*184481*75*2