Problem Statement

There are N dishes, and the i-th dish has a sweetness of A_i and a saltiness of B_i.

Takahashi plans to arrange these N dishes in any order he likes and eat them in that order.

He will eat the dishes in the arranged order, but he will stop eating as soon as the total sweetness of the dishes he has eaten exceeds X or the total saltiness exceeds Y.

Find the minimum possible number of dishes that he will end up eating.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq X, Y \leq 2 \times 10^{14}
• 1 \leq A_i, B_i \leq 10^9
• All input values are integers.

Sample Input 1

4 7 18
2 3 5 1
8 8 1 4

Sample Output 1

2

The i-th dish will be denoted as dish i.

If he arranges the four dishes in the order 2, 3, 1, 4, as soon as he eats dishes 2 and 3, their total sweetness is 8, which is greater than 7. Therefore, in this case, he will end up eating two dishes.

The number of dishes he will eat cannot be 1 or less, so print 2.

Sample Input 2

5 200000000000000 200000000000000
1 1 1 1 1
2 2 2 2 2

Sample Output 2

5

Sample Input 3

8 30 30
1 2 3 4 5 6 7 8
8 7 6 5 4 3 2 1

Sample Output 3

6

Problem Statement

Given an integer N, solve the following problem.

Let f(x)= (The number of positive integers at most x with the same number of digits as x).
Find f(1)+f(2)+\dots+f(N) modulo 998244353.

Constraints

• N is an integer.
• 1 \le N < 10^{18}

Sample Input 1

16

Sample Output 1

73

• For a positive integer x between 1 and 9, the positive integers at most x with the same number of digits as x are 1,2,\dots,x.
  • Thus, we have f(1)=1,f(2)=2,...,f(9)=9.
• For a positive integer x between 10 and 16, the positive integers at most x with the same number of digits as x are 10,11,\dots,x.
  • Thus, we have f(10)=1,f(11)=2,...,f(16)=7.

The final answer is 73.

Sample Input 2

238

Sample Output 2

13870

Sample Input 3

999999999999999999

Sample Output 3

762062362

Be sure to find the sum modulo 998244353.

Problem Statement

You are given a string S consisting of uppercase and lowercase English letters.

We perform the following operation on S 10^{100} times:

• First, create a string T by changing uppercase letters in S to lowercase, and lowercase letters to uppercase.
• Then, concatenate S and T in this order to form a new S.

Answer Q queries. The i-th query is as follows:

• Find the K_i-th character from the beginning of S after all operations are completed.

Constraints

• S is a string consisting of uppercase and lowercase English letters, with length between 1 and 2 \times 10^5, inclusive.
• Q and K_i are integers.
• 1 \le Q \le 2 \times 10^5
• 1 \le K_i \le 10^{18}

Sample Input 1

aB
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Sample Output 1

a B A b A b a B A b a B a B A b

Before the operations, S = aB.

• After performing the operation once on aB, it becomes aBAb.
• After performing the operation twice on aB, it becomes aBAbAbaB.
• \dots

After performing the operation 10^{100} times, S = aBAbAbaBAbaBaBAb...

Sample Input 2

qWeRtYuIoP
8
1 1 2 3 5 8 13 21

Sample Output 2

q q W e t I E Q

Sample Input 3

AnUoHrjhgfLMcDIpzxXmEWPwBZvbKqQuiJTtFSlkNGVReOYCdsay
5
1000000000000000000 123456789 1 987654321 999999999999999999

Sample Output 3

K a A Z L

Problem Statement

We have a connected undirected graph with N vertices and M edges.
The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects Vertices A_i and B_i.

Takahashi is going to remove zero or more edges from this graph.

When removing Edge i, a reward of C_i is given if C_i \geq 0, and a fine of |C_i| is incurred if C_i<0.

Find the maximum total reward that Takahashi can get when the graph must be connected after removing edges.

Constraints

• 2 \leq N \leq 2\times 10^5
• N-1 \leq M \leq 2\times 10^5
• 1 \leq A_i,B_i \leq N
• -10^9 \leq C_i \leq 10^9
• The given graph is connected.
• All values in input are integers.

Sample Input 1

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

Sample Output 1

4

Removing Edges 4 and 5 yields a total reward of 4. You cannot get any more, so the answer is 4.

Sample Input 2

3 3
1 2 1
2 3 0
3 1 -1

Sample Output 2

1

There may be edges that give a negative reward when removed.

Sample Input 3

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

Sample Output 3

5

There may be multi-edges and self-loops.

Problem Statement

There are N people standing in a line, with person i standing at the i-th position from the front.

Repeat the following operation until there is only one person left in the line:

• Remove the person at the front of the line with a probability of \frac{1}{2}, otherwise move them to the end of the line.

For each person i=1,2,\ldots,N, find the probability that person i is the last person remaining in the line, modulo 998244353. (All choices to remove or not are random and independent.)

Constraints

• 2\leq N\leq 3000
• All input values are integers.

Sample Input 1

2

Sample Output 1

332748118 665496236

Person 1 will be the last person remaining in the line with probability \frac{1}{3}.

Person 2 will be the last person remaining in the line with probability \frac{2}{3}.

Sample Input 2

5

Sample Output 2

235530465 792768557 258531487 238597268 471060930