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

In the Kingdom of AtCoder, a week consists of A+B days, with the first through A-th days being holidays and the (A+1)-th through (A+B)-th being weekdays.

Takahashi has N plans, and the i-th plan is scheduled D_i days later.

He has forgotten what day of the week it is today. Determine if it is possible for all of his N plans to be scheduled on holidays.

Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq A,B\leq 10^9
• 1\leq D_1<D_2<\ldots<D_N\leq 10^9

Sample Input 1

3 2 5
1 2 9

Sample Output 1

Yes

In this input, a week consists of seven days, with the first through second days being holidays and the third through seventh days being weekdays.

Let us assume today is the seventh day of the week. In this case, one day later would be the first day of the week, two days later would be the second day of the week, and nine days later would also be the second day of the week, making all plans scheduled on holidays. Therefore, it is possible for all of Takahashi's N plans to be scheduled on holidays.

Sample Input 2

2 5 10
10 15

Sample Output 2

No

Sample Input 3

4 347 347
347 700 705 710

Sample Output 3

Yes

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

A country has N cities and M power plants, which we collectively call places.
The places are numbered 1,2,\dots,N+M, among which Places 1,2,\dots,N are the cities and Places N+1,N+2,\dots,N+M are the power plants.

This country has E power lines. Power Line i (1 \le i \le E) connects Place U_i and Place V_i bidirectionally.
A city is said to be electrified if one can reach at least one of the power plants from the city using some power lines.

Now, Q events will happen. In the i-th (1 \le i \le Q) event, Power Line X_i breaks, making it unusable. Once a power line breaks, it remains broken in the succeeding events.

Find the number of electrified cities right after each events.

Constraints

• All values in input are integers.
• 1 \le N,M
• N+M \le 2 \times 10^5
• 1 \le Q \le E \le 5 \times 10^5
• 1 \le U_i < V_i \le N+M
• If i \neq j, then U_i \neq U_j or V_i \neq V_j.
• 1 \le X_i \le E
• X_i are distinct.

Sample Input 1

5 5 10
2 3
4 10
5 10
6 9
2 9
4 8
1 7
3 6
8 10
1 8
6
3
5
8
10
2
7

Sample Output 1

4
4
2
2
2
1

Initially, all cities are electrified.

• The 1-st event breaks Power Line 3 that connects Point 5 and Point 10.
  • Now City 5 is no longer electrified, while 4 cities remain electrified.
• The 2-nd event breaks Power Line 5 that connects Point 2 and Point 9.
• The 3-rd event breaks Power Line 8 that connects Point 3 and Point 6.
  • Now Cities 2 and 3 are no longer electrified, while 2 cities remain electrified.
• The 4-th event breaks Power Line 10 that connects Point 1 and Point 8.
• The 5-th event breaks Power Line 2 that connects Point 4 and Point 10.
• The 6-th event breaks Power Line 7 that connects Point 1 and Point 7.
  • Now City 1 is no longer electrified, while 1 city remains electrified.

Problem Statement

We have N dice. For each i = 1, 2, \ldots, N, when the i-th die is thrown, it shows a random integer between 1 and A_i, inclusive, with equal probability.

Find the probability, modulo 998244353, that the following condition is satisfied when the N dice are thrown simultaneously.

There is a way to choose some (possibly all) of the N dice so that the sum of their results is 10.

Constraints

• 1 \leq N \leq 100
• 1 \leq A_i \leq 10^6
• All input values are integers.

Sample Input 1

4
1 7 2 9

Sample Output 1

942786334

For instance, if the first, second, third, and fourth dice show 1, 3, 2, and 7, respectively, these results satisfy the condition. In fact, if the second and fourth dice are chosen, the sum of their results is 3 + 7 = 10. Alternatively, if the first, third, and fourth dice are chosen, the sum of their results is 1 + 2 + 7 = 10.

On the other hand, if the first, second, third, and fourth dice show 1, 6, 1, and 5, respectively, there is no way to choose some of them so that the sum of their results is 10, so the condition is not satisfied.

In this sample input, the probability of the results of the N dice satisfying the condition is \frac{11}{18}. Thus, print this value modulo 998244353, that is, 942786334.

Sample Input 2

7
1 10 100 1000 10000 100000 1000000

Sample Output 2

996117877