Problem Statement

How many triples of non-negative integers (a, b, c) satisfy a+b+c \leq S and a \times b \times c \leq T?

Constraints

• 0 \leq S \leq 100
• 0 \leq T \leq 10000
• S and T are integers.

Sample Input 1

1 0

Sample Output 1

4

The triples (a,b,c) satisfying the conditions are (0,0,0), (0,0,1), (0,1,0), and (1,0,0) ― there are four of them.

Sample Input 2

2 5

Sample Output 2

10

Sample Input 3

10 10

Sample Output 3

213

Sample Input 4

30 100

Sample Output 4

2471

Problem Statement

You are given a simple undirected graph with N vertices and M edges. The vertices are numbered 1, \dots, N, and the i-th (1 \leq i \leq M) edge connects Vertex U_i and Vertex V_i.

Find the number of tuples of integers a, b, c that satisfy all of the following conditions:

• 1 \leq a \lt b \lt c \leq N
• There is an edge connecting Vertex a and Vertex b.
• There is an edge connecting Vertex b and Vertex c.
• There is an edge connecting Vertex c and Vertex a.

Constraints

• 3 \leq N \leq 100
• 1 \leq M \leq \frac{N(N - 1)}{2}
• 1 \leq U_i \lt V_i \leq N \, (1 \leq i \leq M)
• (U_i, V_i) \neq (U_j, V_j) \, (i \neq j)
• All values in input are integers.

Sample Input 1

5 6
1 5
4 5
2 3
1 4
3 5
2 5

Sample Output 1

2

(a, b, c) = (1, 4, 5), (2, 3, 5) satisfy the conditions.

Sample Input 2

3 1
1 2

Sample Output 2

0

Sample Input 3

7 10
1 7
5 7
2 5
3 6
4 7
1 5
2 4
1 3
1 6
2 7

Sample Output 3

4

Problem Statement

N balls are lined up in a row from left to right. Initially, the i-th (1 \leq i \leq N) ball from the left has an integer i written on it.

Takahashi has performed Q operations. The i-th (1 \leq i \leq Q) operation was as follows.

• Swap the ball with the integer x_i written on it with the next ball to the right. If the ball with the integer x_i written on it was originally the rightmost ball, swap it with the next ball to the left instead.

Let a_i be the integer written on the i-th (1 \leq i \leq N) ball after the operations. Find a_1,\ldots,a_N.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq Q \leq 2 \times 10^5
• 1 \leq x_i \leq N
• All values in input are integers.

Sample Input 1

5 5
1
2
3
4
5

Sample Output 1

1 2 3 5 4

The operations are performed as follows.

• Swap the ball with 1 written on it with the next ball to the right. Now, the balls have integers 2,1,3,4,5 written on them, from left to right.
• Swap the ball with 2 written on it with the next ball to the right. Now, the balls have integers 1,2,3,4,5 written on them, from left to right.
• Swap the ball with 3 written on it with the next ball to the right. Now, the balls have integers 1,2,4,3,5 written on them, from left to right.
• Swap the ball with 4 written on it with the next ball to the right. Now, the balls have integers 1,2,3,4,5 written on them, from left to right.
• Swap the ball with 5 written on it with the next ball to the left, since it is the rightmost ball. Now, the balls have integers 1,2,3,5,4 written on them, from left to right.

Sample Input 2

7 7
7
7
7
7
7
7
7

Sample Output 2

1 2 3 4 5 7 6

Sample Input 3

10 6
1
5
2
9
6
6

Sample Output 3

1 2 3 4 5 7 6 8 10 9

Problem Statement

We have a multiset of integers S, which is initially empty.

Given Q queries, process them in order. Each query is of one of the following types.

• 1 x: Insert an x into S.

• 2 x c: Remove an x from S m times, where m = \mathrm{min}(c,( the number of x's contained in S)).

• 3 : Print ( maximum value of S)-( minimum value of S). It is guaranteed that S is not empty when this query is given.

Constraints

• 1 \leq Q \leq 2\times 10^5
• 0 \leq x \leq 10^9
• 1 \leq c \leq Q
• When a query of type 3 is given, S is not empty.
• All values in input are integers.

Sample Input 1

8
1 3
1 2
3
1 2
1 7
3
2 2 3
3

Sample Output 1

1
5
4

The multiset S transitions as follows.

• 1-st query: insert 3 into S. S is now \lbrace 3 \rbrace.
• 2-nd query: insert 2 into S. S is now \lbrace 2, 3 \rbrace.
• 3-rd query: the maximum value of S = \lbrace 2, 3\rbrace is 3 and its minimum value is 2, so print 3-2=1.
• 4-th query: insert 2 into S. S is now \lbrace 2,2,3 \rbrace.
• 5-th query: insert 7 into S. S is now \lbrace 2, 2,3, 7\rbrace.
• 6-th query: the maximum value of S = \lbrace 2,2,3, 7\rbrace is 7 and its minimum value is 2, so print 7-2=5.
• 7-th query: since there are two 2's in S and \mathrm{min(2,3)} = 2, remove 2 from S twice. S is now \lbrace 3, 7\rbrace.
• 8-th query: the maximum value of S = \lbrace 3, 7\rbrace is 7 and its minimum value is 3, so print 7-3=4.

Sample Input 2

4
1 10000
1 1000
2 100 3
1 10

Sample Output 2

If the given queries do not contain that of type 3, nothing should be printed.

Problem Statement

You are given an integer W.
You are going to prepare some weights so that all of the conditions below are satisfied.

• The number of weights is between 1 and 300, inclusive.
• Each weight has a mass of positive integer not exceeding 10^6.
• Every integer between 1 and W, inclusive, is a good integer. Here, a positive integer n is said to be a good integer if the following condition is satisfied:
  • We can choose at most 3 different weights from the prepared weights with a total mass of n.

Print a combination of weights that satisfies the conditions.

Constraints

• 1 \leq W \leq 10^6
• W is an integer.

Sample Input 1

6

Sample Output 1

3
1 2 3

In the output above, 3 weights with masses 1, 2, and 3 are prepared.
This output satisfies the conditions. Especially, regarding the 3-rd condition, we can confirm that every integer between 1 and W, inclusive, is a good integer.

• If we choose only the 1-st weight, it has a total mass of 1.
• If we choose only the 2-nd weight, it has a total mass of 2.
• If we choose only the 3-rd weight, it has a total mass of 3.
• If we choose the 1-st and the 3-rd weights, they have a total mass of 4.
• If we choose the 2-nd and the 3-rd weights, they have a total mass of 5.
• If we choose the 1-st, the 2-nd, and the 3-rd weights, they have a total mass of 6.

Sample Input 2

12

Sample Output 2

6
2 5 1 2 5 1

You may prepare multiple weights with the same mass.