Problem Statement

You are given a sequence A=(A_1,A_2,\ldots,A_N) of length N consisting of non-negative integers.

Determine if there is an even number represented as the sum of two different elements of A. If it exists, find the maximum such number.

Constraints

• 2\leq N \leq 2\times 10^5
• 0\leq A_i\leq 10^9
• The elements of A are distinct.
• All values in the input are integers.

Sample Input 1

3
2 3 4

Sample Output 1

6

The values represented as the sum of two distinct elements of A are 5, 6, and 7. We have an even number here, and the maximum is 6.

Sample Input 2

2
1 0

Sample Output 2

-1

The value represented as the sum of two distinct elements of A is 1. We have no even number here, so -1 should be printed.

Problem Statement

There is a class with N students. The height of the i-th student (1 \leq i \leq N) is A_i.

For each j=1,2,\ldots,Q, answer the following question.

• How many of the N students have a height of at least x_j?

Constraints

• 1 \leq N,Q \leq 2 \times 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq x_j \leq 10^9
• All values in input are integers.

Sample Input 1

3 1
100 160 130
120

Sample Output 1

2

The students with a height of at least 120 are the 2-nd and 3-rd ones.

Sample Input 2

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

Sample Output 2

0
1
2
3
4

Sample Input 3

5 5
804289384 846930887 681692778 714636916 957747794
424238336
719885387
649760493
596516650
189641422

Sample Output 3

5
3
5
5
5

Problem Statement

You are given a sequence A = (A_1, A_2, \dots, A_N) of length N.

Given Q queries, process all of them in order. The q-th (1\leq q\leq Q) query is in one of the following three formats, which represents the following queries:

• 1\ x _ q: assign x_q to every element of A.
• 2\ i _ q\ x _ q: add x_q to A _ {i _ q}.
• 3\ i _ q: print the value of A _ {i _ q}.

Constraints

• 1 \leq N \leq 2\times10^5
• 1 \leq Q \leq 2\times10^5
• 0 \leq A _ i \leq 10^9\ (1\leq i\leq N)
• If the q-th (1\leq q\leq Q) query is in the second or third format, 1 \leq i _ q \leq N.
• If the q-th (1\leq q\leq Q) query is in the first or second format, 0 \leq x _ q \leq 10^9.
• There exists a query in the third format.
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

1
8
5

Initially, A=(3,1,4,1,5). The queries are processed as follows:

• A_2=1, so print 1.
• Add 4 to A_3, making A=(3,1,8,1,5).
• A_3=8, so print 8.
• Assign 1 to every element of A, making A=(1,1,1,1,1).
• Add 4 to A_3, making A=(1,1,5,1,1).
• A_3=5, so print 5.

Sample Input 2

1
1000000000
8
2 1 1000000000
2 1 1000000000
2 1 1000000000
2 1 1000000000
2 1 1000000000
2 1 1000000000
2 1 1000000000
3 1

Sample Output 2

8000000000

Note that the elements of A may not fit into a 32-bit integer type.

Sample Input 3

10
1 8 4 15 7 5 7 5 8 0
20
2 7 0
3 7
3 8
1 7
3 3
2 4 4
2 4 9
2 10 5
1 10
2 4 2
1 10
2 3 1
2 8 11
2 3 14
2 1 9
3 8
3 8
3 1
2 6 5
3 7

Sample Output 3

7
5
7
21
21
19
10

Problem Statement

AtCoder cafeteria sells meals consisting of a main dish and a side dish.
There are N types of main dishes, called main dish 1, main dish 2, \dots, main dish N. Main dish i costs a_i yen.
There are M types of side dishes, called side dish 1, side dish 2, \dots, side dish M. Side dish i costs b_i yen.

A set meal is composed by choosing one main dish and one side dish. The price of a set meal is the sum of the prices of the chosen main dish and side dish.
However, for L distinct pairs (c_1, d_1), \dots, (c_L, d_L), the set meal consisting of main dish c_i and side dish d_i is not offered because they do not go well together.
That is, NM - L set meals are offered. (The constraints guarantee that at least one set meal is offered.)

Find the price of the most expensive set meal offered.

Constraints

• 1 \leq N, M \leq 10^5
• 0 \leq L \leq \min(10^5, NM - 1)
• 1 \leq a_i, b_i \leq 10^9
• 1 \leq c_i \leq N
• 1 \leq d_j \leq M
• (c_i, d_i) \neq (c_j, d_j) if i \neq j.
• All input values are integers.

Sample Input 1

2 3 3
2 1
10 30 20
1 2
2 1
2 3

Sample Output 1

31

They offer three set meals, listed below, along with their prices:

• A set meal consisting of main dish 1 and side dish 1, at a price of 2 + 10 = 12 yen.
• A set meal consisting of main dish 1 and side dish 3, at a price of 2 + 20 = 22 yen.
• A set meal consisting of main dish 2 and side dish 2, at a price of 1 + 30 = 31 yen.

Among them, the most expensive is the third one. Thus, print 31.

Sample Input 2

2 1 0
1000000000 1
1000000000

Sample Output 2

2000000000

Sample Input 3

10 10 10
47718 21994 74148 76721 98917 73766 29598 59035 69293 29127
7017 46004 16086 62644 74928 57404 32168 45794 19493 71590
1 3
2 6
4 5
5 4
5 5
5 6
5 7
5 8
5 10
7 3

Sample Output 3

149076

Problem Statement

Consider placing B black rooks and W white rooks on a grid with N horizontal rows and M vertical columns.

A placement of the rooks satisfying all of the following conditions is called a good placement.

• All B+W rooks are placed on the grid.
• At most one rook is placed in the same square.
• There is no pair of white rook and black rook attacking each other. That is, there is no pair of white rook and black rook such that one of them can reach the square in which the other is placed in one move.

Here, in one move, a rook can reach any square that is on a horizontal or vertical line from its current position and is reachable without jumping over another rook.

How many good placements are there? Since this count can be enormous, print it modulo 998244353.

Rooks in the same color are not distinguished.

Constraints

• 1 \leq N,M \leq 50
• 1 \leq B,W \leq 2500
• B+W \leq N \times M
• All values in input are integers.

Sample Input 1

2 2 1 1

Sample Output 1

4

There are four good placements as follows.

Sample Input 2

1 2 1 1

Sample Output 2

0

There may be no good placement.

Sample Input 3

40 40 30 30

Sample Output 3

467620384

Be sure to print the count modulo 998244353.