Problem Statement

N students took an exam. The students are labeled as Student 1, Student 2, \dots, Student N, and Student i scored a_i points.

A student who scored less than P points are considered to have failed the exam and cannot earn the credit. Find the number of students who failed the exam.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq P \leq 100
• 0 \leq a_i \leq 100 (1 \leq i \leq N)
• All values in input are integers.

Sample Input 1

4 50
80 60 40 0

Sample Output 1

2

Students 1 and 2, who scored 80 and 60 points, respectively, succeeded in scoring at least 50 points to earn the credit.
On the other hand, Students 3 and 4, who scored 40 and 0 points, respectively, fell below 50 points and failed the exam. Thus, the answer is 2.

Sample Input 2

3 90
89 89 89

Sample Output 2

3

Sample Input 3

2 22
6 37

Sample Output 3

1

Problem Statement

You are given a positive integer N.

We have a grid with N rows and N columns, where the square at the i-th row from the top and j-th column from the left has a digit A_{i,j} written on it.

Assume that the upper and lower edges of this grid are connected, as well as the left and right edges. In other words, all of the following holds.

• (N,i) is just above (1,i), and (1,i) is just below (N,i). (1\le i\le N).
• (i,N) is just to the left of (i,1), and (i,1) is just to the right of (i,N). (1\le i\le N).

Takahashi will first choose one of the following eight directions: up, down, left, right, and the four diagonal directions. Then, he will start on a square of his choice and repeat moving one square in the chosen direction N-1 times.

In this process, Takahashi visits N squares. Find the greatest possible value of the integer that is obtained by arranging the digits written on the squares visited by Takahashi from left to right in the order visited by him.

Constraints

• 1 \le N \le 10
• 1 \le A_{i,j} \le 9
• All values in input are integers.

Sample Input 1

4
1161
1119
7111
1811

Sample Output 1

9786

If Takahashi starts on the square at the 2-nd row from the top and 4-th column from the left and goes down and to the right, the integer obtained by arranging the digits written on the visited squares will be 9786. It is impossible to make a value greater than 9786, so the answer is 9786.

Sample Input 2

10
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111

Sample Output 2

1111111111

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

Problem Statement

We have a sequence of N numbers: A = (a_1, a_2, \dots, a_N).
Process the Q queries explained below.

• Query i: You are given a pair of integers (x_i, k_i). Let us look at the elements of A one by one from the beginning: a_1, a_2, \dots Which element will be the k_i-th occurrence of the number x_i?
  Print the index of that element, or -1 if there is no such element.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq Q \leq 2 \times 10^5
• 0 \leq a_i \leq 10^9 (1 \leq i \leq N)
• 0 \leq x_i \leq 10^9 (1 \leq i \leq Q)
• 1 \leq k_i \leq N (1 \leq i \leq Q)
• All values in input are integers.

Sample Input 1

6 8
1 1 2 3 1 2
1 1
1 2
1 3
1 4
2 1
2 2
2 3
4 1

Sample Output 1

1
2
5
-1
3
6
-1
-1

1 occurs in A at a_1, a_2, a_5. Thus, the answers to Query 1 through 4 are 1, 2, 5, -1 in this order.

Sample Input 2

3 2
0 1000000000 999999999
1000000000 1
123456789 1

Sample Output 2

2
-1

Problem Statement

You are given N strings S_1,S_2,\dots,S_N, each of length M, consisting of lowercase English letter. Here, S_i are pairwise distinct.

Determine if one can rearrange these strings to obtain a new sequence of strings T_1,T_2,\dots,T_N such that:

• for all integers i such that 1 \le i \le N-1, one can alter exactly one character of T_i to another lowercase English letter to make it equal to T_{i+1}.

Constraints

• 2 \le N \le 8
• 1 \le M \le 5
• S_i is a string of length M consisting of lowercase English letters. (1 \le i \le N)
• S_i are pairwise distinct.

Sample Input 1

4 4
bbed
abcd
abed
fbed

Sample Output 1

Yes

One can rearrange them in this order: abcd, abed, bbed, fbed. This sequence satisfies the condition.

Sample Input 2

2 5
abcde
abced

Sample Output 2

No

No matter how the strings are rearranged, the condition is never satisfied.

Sample Input 3

8 4
fast
face
cast
race
fact
rice
nice
case

Sample Output 3

Yes

Problem Statement

There are N people numbered 1 to N on a coordinate plane.
Person 1 is at the origin.

You are given M pieces of information in the following form:

• From person A_i's perspective, person B_i is X_i units away in the positive x-direction and Y_i units away in the positive y-direction.

Determine the coordinates of each person. If the coordinates of a person cannot be uniquely determined, report that fact.

Constraints

• 1 \leq N \leq 2\times 10^5
• 0 \leq M \leq 2\times 10^5
• 1\leq A_i, B_i \leq N
• A_i \neq B_i
• -10^9 \leq X_i,Y_i \leq 10^9
• All input values are integers.
• The given information is consistent.

Sample Input 1

3 2
1 2 2 1
1 3 -1 -2

Sample Output 1

0 0
2 1
-1 -2

The figure below shows the positional relationship of the three people.

Sample Input 2

3 2
2 1 -2 -1
2 3 -3 -3

Sample Output 2

0 0
2 1
-1 -2

The figure below shows the positional relationship of the three people.

Sample Input 3

5 7
1 2 0 0
1 2 0 0
2 3 0 0
3 1 0 0
2 1 0 0
3 2 0 0
4 5 0 0

Sample Output 3

0 0
0 0
0 0
undecidable
undecidable

The same piece of information may be given multiple times, and multiple people may be at the same coordinates.