Problem Statement

Takahashi and Aoki decided to jog.
Takahashi repeats the following: "walk at B meters a second for A seconds and take a rest for C seconds."
Aoki repeats the following: "walk at E meters a second for D seconds and take a rest for F seconds."
When X seconds have passed since they simultaneously started to jog, which of Takahashi and Aoki goes ahead?

Constraints

• 1 \leq A, B, C, D, E, F, X \leq 100
• All values in input are integers.

Sample Input 1

4 3 3 6 2 5 10

Sample Output 1

Takahashi

During the first 10 seconds after they started to jog, they move as follows.

• Takahashi walks for 4 seconds, takes a rest for 3 seconds, and walks again for 3 seconds. As a result, he advances a total of (4 + 3) \times 3 = 21 meters.
• Aoki walks for 6 seconds and takes a rest for 4 seconds. As a result, he advances a total of 6 \times 2 = 12 meters.

Since Takahashi goes ahead, Takahashi should be printed.

Sample Input 2

3 1 4 1 5 9 2

Sample Output 2

Aoki

Sample Input 3

1 1 1 1 1 1 1

Sample Output 3

Draw

Problem Statement

Takahashi wants to send a letter to Santa Claus. He has an envelope with an X-yen (Japanese currency) stamp stuck on it.
To be delivered to Santa Claus, the envelope must have stamps in a total value of at least Y yen.
Takahashi will put some more 10-yen stamps so that the envelope will have stamps worth at least Y yen in total.
At least how many more 10-yen stamps does Takahashi need to put on the envelope?

Constraints

• X and Y are integers.
• 1 \le X,Y \le 1000

Sample Input 1

80 94

Sample Output 1

2

• After adding zero 10-yen stamps to the 80-yen stamp, the total is 80 yen, which is less than the required amount of 94 yen.
• After adding one 10-yen stamp to the 80-yen stamp, the total is 90 yen, which is less than the required amount of 94 yen.
• After adding two 10-yen stamps to the 80-yen stamp, the total is 100 yen, which is not less than the required amount of 94 yen.

Sample Input 2

1000 63

Sample Output 2

0

The envelope may already have a stamp with enough value.

Sample Input 3

270 750

Sample Output 3

48

Problem Statement

There are 7 points A, B, C, D, E, F, and G on a straight line, in this order. (See also the figure below.)
The distances between adjacent points are as follows.

• Between A and B: 3
• Between B and C: 1
• Between C and D: 4
• Between D and E: 1
• Between E and F: 5
• Between F and G: 9

You are given two uppercase English letters p and q. Each of p and q is A, B, C, D, E, F, or G, and it holds that p \neq q.
Find the distance between the points p and q.

Constraints

• Each of p and q is A,B,C,D,E,F, or G.
• p \neq q

Sample Input 1

A C

Sample Output 1

4

The distance between the points A and C is 3 + 1 = 4.

Sample Input 2

G B

Sample Output 2

20

The distance between the points G and B is 9 + 5 + 1 + 4 + 1 = 20.

Sample Input 3

C F

Sample Output 3

10

Problem Statement

We have a sequence of length N consisting of positive integers: A=(A_1,\ldots,A_N). Any two adjacent terms have different values.

Let us insert some numbers into this sequence by the following procedure.

1. If every pair of adjacent terms in A has an absolute difference of 1, terminate the procedure.
2. Let A_i, A_{i+1} be the pair of adjacent terms nearest to the beginning of A whose absolute difference is not 1.
   • If A_i < A_{i+1}, insert A_i+1,A_i+2,\ldots,A_{i+1}-1 between A_i and A_{i+1}.
   • If A_i > A_{i+1}, insert A_i-1,A_i-2,\ldots,A_{i+1}+1 between A_i and A_{i+1}.
3. Return to step 1.

Print the sequence when the procedure ends.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 100
• A_i \neq A_{i+1}
• All values in the input are integers.

Sample Input 1

4
2 5 1 2

Sample Output 1

2 3 4 5 4 3 2 1 2

The initial sequence is (2,5,1,2). The procedure goes as follows.

• Insert 3,4 between the first term 2 and the second term 5, making the sequence (2,3,4,5,1,2).
• Insert 4,3,2 between the fourth term 5 and the fifth term 1, making the sequence (2,3,4,5,4,3,2,1,2).

Sample Input 2

6
3 4 5 6 5 4

Sample Output 2

3 4 5 6 5 4

No insertions may be performed.

Problem Statement

We have HW cards arranged in a matrix with H rows and W columns.
For each i=1, \ldots, N, the card at the A_i-th row from the top and B_i-th column from the left has a number i written on it. The other HW-N cards have nothing written on them.

We will repeat the following two kinds of operations on these cards as long as we can.

• If there is a row without a numbered card, remove all the cards in that row and fill the gap by shifting the remaining cards upward.
• If there is a column without a numbered card, remove all the cards in that column and fill the gap by shifting the remaining cards to the left.

Find the position of each numbered card after the end of the process above. It can be proved that these positions are uniquely determined without depending on the order in which the operations are done.

Constraints

• 1 \leq H,W \leq 10^9
• 1 \leq N \leq \min(10^5,HW)
• 1 \leq A_i \leq H
• 1 \leq B_i \leq W
• All pairs (A_i,B_i) are distinct.
• All values in input are integers.

Sample Input 1

4 5 2
3 2
2 5

Sample Output 1

2 1
1 2

Let * represent a card with nothing written on it. The initial arrangement of cards is:

*****
****2
*1***
*****

After the end of the process, they will be arranged as follows:

*2
1*

Here, the card with 1 is at the 2-nd row from the top and 1-st column from the left, and the card with 2 is at the 1-st row from the top and 2-nd column from the left.

Sample Input 2

1000000000 1000000000 10
1 1
10 10
100 100
1000 1000
10000 10000
100000 100000
1000000 1000000
10000000 10000000
100000000 100000000
1000000000 1000000000

Sample Output 2

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

Problem Statement

You are given positive integers N and Q, and a string S of length N consisting of lowercase English letters.

Process Q queries. Each query is of one of the following two types.

• 1 x: Perform the following x times in a row: delete the last character of S and append it to the beginning.
• 2 x: Print the x-th character of S.

Constraints

• 2 \le N \le 5 \times 10^5
• 1 \le Q \le 5 \times 10^5
• 1 \le x \le N
• |S|=N
• S consists of lowercase English letters.
• At least one query in the format 2 x.
• N, Q, x are all integers.

Sample Input 1

3 3
abc
2 2
1 1
2 2

Sample Output 1

b
a

In the 1-st query, S is abc, so the 2-nd character b should be printed. In the 2-nd query, S is changed from abc to cab. In the 3-rd query, S is cab, so the 2-nd character a should be printed.

Sample Input 2

10 8
dsuccxulnl
2 4
2 7
1 2
2 7
1 1
1 2
1 3
2 5

Sample Output 2

c
u
c
u

Problem Statement

We have a string S. Initially, S= 1.
Process Q queries in the following formats in order.

• 1 x : Append a digit x at the end of S.
• 2 : Delete the digit at the beginning of S.
• 3 : Print the number represented by S in decimal, modulo 998244353.

Constraints

• 1 \leq Q \leq 6 \times 10^5
• For each query in the first format, x \in \{1,2,3,4,5,6,7,8,9\}.
• A query in the second format is given only if S has a length of 2 or greater.
• There is at least one query in the third format.

Sample Input 1

3
3
1 2
3

Sample Output 1

1
12

In the first query, S is 1, so you should print 1 modulo 998244353, that is, 1.
In the second query, S becomes 12.
In the third query, S is 12, so you should print 12 modulo 998244353, that is, 12.

Sample Input 2

3
1 5
2
3

Sample Output 2

5

Sample Input 3

11
1 9
1 9
1 8
1 2
1 4
1 4
1 3
1 5
1 3
2
3

Sample Output 3

0

Be sure to print numbers modulo 998244353.

Problem Statement

In the country of AtCoder, there are N stations: station 1, station 2, \ldots, station N.

You are given M pieces of information about trains in the country. The i-th piece of information (1\leq i\leq M) is represented by a tuple of six positive integers (l _ i,d _ i,k _ i,c _ i,A _ i,B _ i), which corresponds to the following information:

• For each t=l _ i,l _ i+d _ i,l _ i+2d _ i,\ldots,l _ i+(k _ i-1)d _ i, there is a train as follows:
  • The train departs from station A _ i at time t and arrives at station B _ i at time t+c _ i.

No trains exist other than those described by this information, and it is impossible to move from one station to another by any means other than by train.
Also, assume that the time required for transfers is negligible.

Let f(S) be the latest time at which one can arrive at station N from station S.
More precisely, f(S) is defined as the maximum value of t for which there is a sequence of tuples of four integers \big((t _ i,c _ i,A _ i,B _ i)\big) _ {i=1,2,\ldots,k} that satisfies all of the following conditions:

• t\leq t _ 1
• A _ 1=S,B _ k=N
• B _ i=A _ {i+1} for all 1\leq i\lt k,
• For all 1\leq i\leq k, there is a train that departs from station A _ i at time t _ i and arrives at station B _ i at time t _ i+c _ i.
• t _ i+c _ i\leq t _ {i+1} for all 1\leq i\lt k.

If no such t exists, set f(S)=-\infty.

Find f(1),f(2),\ldots,f(N-1).

Constraints

• 2\leq N\leq2\times10 ^ 5
• 1\leq M\leq2\times10 ^ 5
• 1\leq l _ i,d _ i,k _ i,c _ i\leq10 ^ 9\ (1\leq i\leq M)
• 1\leq A _ i,B _ i\leq N\ (1\leq i\leq M)
• A _ i\neq B _ i\ (1\leq i\leq M)
• All input values are integers.

Sample Input 1

6 7
10 5 10 3 1 3
13 5 10 2 3 4
15 5 10 7 4 6
3 10 2 4 2 5
7 10 2 3 5 6
5 3 18 2 2 3
6 3 20 4 2 1

Sample Output 1

55
56
58
60
17

The following diagram shows the trains running in the country (information about arrival and departure times is omitted).

Consider the latest time at which one can arrive at station 6 from station 2. As shown in the following diagram, one can arrive at station 6 by departing from station 2 at time 56 and moving as station 2\rightarrow station 3\rightarrow station 4\rightarrow station 6.

It is impossible to depart from station 2 after time 56 and arrive at station 6, so f(2)=56.

Sample Input 2

5 5
1000000000 1000000000 1000000000 1000000000 1 5
5 9 2 6 2 3
10 4 1 6 2 3
1 1 1 1 3 5
3 1 4 1 5 1

Sample Output 2

1000000000000000000
Unreachable
1
Unreachable

There is a train that departs from station 1 at time 10 ^ {18} and arrives at station 5 at time 10 ^ {18}+10 ^ 9. There are no trains departing from station 1 after that time, so f(1)=10 ^ {18}. As seen here, the answer may not fit within a 32\operatorname{bit} integer.

Also, both the second and third pieces of information guarantee that there is a train that departs from station 2 at time 14 and arrives at station 3 at time 20. As seen here, some trains may appear in multiple pieces of information.

Sample Input 3

16 20
4018 9698 2850 3026 8 11
2310 7571 7732 1862 13 14
2440 2121 20 1849 11 16
2560 5115 190 3655 5 16
1936 6664 39 8822 4 16
7597 8325 20 7576 12 5
5396 1088 540 7765 15 1
3226 88 6988 2504 13 5
1838 7490 63 4098 8 3
1456 5042 4 2815 14 7
3762 6803 5054 6994 10 9
9526 6001 61 8025 7 8
5176 6747 107 3403 1 5
2014 5533 2031 8127 8 11
8102 5878 58 9548 9 10
3788 174 3088 5950 3 13
7778 5389 100 9003 10 15
556 9425 9458 109 3 11
5725 7937 10 3282 2 9
6951 7211 8590 1994 15 12

Sample Output 3

720358
77158
540926
255168
969295
Unreachable
369586
466218
343148
541289
42739
165772
618082
16582
591828

Problem Statement

This is an interactive task, where your and the judge's programs interact via Standard Input and Output.

You and the judge will follow the procedure below. The procedure consists of phases 1 and 2; phase 1 is immediately followed by phase 2.

(Phase 1)

• The judge gives you an integer N.
• You print an integer M between 1 and 50000, inclusive.
• You also print M pairs of integers (l_1, r_1), (l_2, r_2), \ldots, (l_M, r_M) such that 1 \leq l_i \leq r_i \leq N for every i = 1, 2, \ldots, M (the M pairs do not have to be distinct).

(Phase 2)

• The judge gives you an integer Q.
• You and the judge repeats the following Q times.
  • The judge gives you two integers L and R as a query.
  • You respond with two integers a and b between 1 and M, inclusive (possibly with a = b). Here, a and b must satisfy the condition below. Otherwise, your submission will be judged incorrect.
    • The union of the set \lbrace l_a, l_a+1, \ldots, r_a\rbrace and the set \lbrace l_b, l_b+1, \ldots, r_b\rbrace equals the set \lbrace L, L+1, \ldots, R\rbrace.

After the procedure above, terminate the program immediately to be judged correct.

Constraints

• 1 \leq N \leq 4000
• 1 \leq Q \leq 10^5
• 1 \leq L \leq R \leq N
• All values in the input are integers.

Input and Output

This is an interactive task, where your and the judge's programs interact via Standard Input and Output.

(Phase 1)

• First, N is given from the input.
• Next, an integer M between 1 and 50000, inclusive, should be printed.
• Then, (l_1, r_1), (l_2, r_2), \ldots, (l_M, r_M) should be printed, one at a time. Specifically, for each i = 1, 2, \ldots, M, the i-th output should be (l_i, r_i) in the following format:

l_i r_i

(Phase 2)

• First, Q is given from the input.
• In each query, integers L and R representing the query are given in the following format:

L R

• In response to each query, two integers a and b should be printed in the following format:

a b

Cautions

• At the end of each output, print a newline and flush Standard Output. Otherwise, you may get the TLE verdict.
• If your program prints a malformed output or quits prematurely, the verdict will be indeterminate. Particularly, note that in case of a runtime error, the verdict may be WA or TLE instead of RE.
• After phase 2, immediately terminate the program. Otherwise, the verdict will be indeterminate.
• L and R given in phase 2 will be decided according to (l_1, r_1), (l_2, r_2), \ldots, (l_M, r_M) you print in phase 1.

Sample Interaction

Below is a sample interaction with N = 4 and Q = 4.