Problem Statement

Given a non-negative integer X, perform the following operation for i=1,2,\dots,K in this order and find the resulting X.

• Round X off to the nearest 10^i.
  • Formally, replace X with Y that is "the largest multiple of 10^i that minimizes |Y-X|."
  • Here are some examples:
    • Rounding 273 off to the nearest 10^2 yields 300.
    • Rounding 999 off to the nearest 10^3 yields 1000.
    • Rounding 100 off to the nearest 10^{10} yields 0.
    • Rounding 1015 off to the nearest 10^1 yields 1020.

Constraints

• X and K are integers.
• 0 \le X < 10^{15}
• 1 \le K \le 15

Sample Input 1

2048 2

Sample Output 1

2100

X changes as 2048 \rightarrow 2050 \rightarrow 2100 by the operations.

Sample Input 2

1 15

Sample Output 2

0

Sample Input 3

999 3

Sample Output 3

1000

Sample Input 4

314159265358979 12

Sample Output 4

314000000000000

X may not fit into a 32-bit integer type.

Problem Statement

You are given integers A and B, in base K.
Print A \times B in decimal.

Notes

For base-K representation, see Wikipedia's article on Positional notation.

Constraints

• 2 \leq K \leq 10
• 1 \leq A,B \leq 10^5
• A and B are in base-K representation.

Sample Input 1

2
1011 10100

Sample Output 1

220

1011 in base 2 corresponds to 11 in base 10.
10100 in base 2 corresponds to 20 in base 10.
We have 11 \times 20 = 220, so print 220.

Sample Input 2

7
123 456

Sample Output 2

15642

123 in base 7 corresponds to 66 in base 10.
456 in base 7 corresponds to 237 in base 10.
We have 66 \times 237 = 15642, so print 15642.

Problem Statement

We have N boxes numbered 1 to N that are initially empty, and an unlimited number of blank cards.
Process Q queries in order. There are three kinds of queries as follows.

• 1 i j \colon Write the number i on a blank card and put it into box j.
• 2 i \colon Report all numbers written on the cards in box i, in ascending order.
• 3 i \colon Report all box numbers of the boxes that contain a card with the number i, in ascending order.

Here, note the following.

• In a query of the second kind, if box i contains multiple cards with the same number, that number should be printed the number of times equal to the number of those cards.
• In a query of the third kind, even if a box contains multiple cards with the number i, the box number of that box should be printed only once.

Constraints

• 1 \leq N, Q \leq 2 \times 10^5
• For a query of the first kind:
  • 1 \leq i \leq 2 \times 10^5
  • 1 \leq j \leq N
• For a query of the second kind:
  • 1 \leq i \leq N
  • Box i contains some cards when this query is given.
• For a query of the third kind:
  • 1 \leq i \leq 2 \times 10^5
  • Some boxes contain a card with the number i when this query is given.
• At most 2 \times 10^5 numbers are to be reported.
• All values in the input are integers.

Sample Input 1

5
8
1 1 1
1 2 4
1 1 4
2 4
1 1 4
2 4
3 1
3 2

Sample Output 1

1 2
1 1 2
1 4
4

Let us process the queries in order.

• Write 1 on a card and put it into box 1.
• Write 2 on a card and put it into box 4.
• Write 1 on a card and put it into box 4.
• Box 4 contains cards with the numbers 1 and 2.
  • Print 1 and 2 in this order.
• Write 1 on a card and put it into box 4.
• Box 4 contains cards with the numbers 1, 1, and 2.
  • Note that you should print 1 twice.
• Boxes 1 and 4 contain a card with the number 1.
  • Note that you should print 4 only once, even though box 4 contains two cards with the number 1.
• Boxes 4 contains a card with the number 2.

Sample Input 2

1
5
1 1 1
1 2 1
1 200000 1
2 1
3 200000

Sample Output 2

1 2 200000
1

Problem Statement

You are given two sequences: A=(A_1,A_2, \ldots ,A_N) consisting of N positive integers, and B=(B_1, \ldots ,B_M) consisting of M positive integers.

Find the minimum difference of an element of A and an element of B, that is, \displaystyle \min_{ 1\leq i\leq N}\displaystyle\min_{1\leq j\leq M} \lvert A_i-B_j\rvert.

Constraints

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

Sample Input 1

2 2
1 6
4 9

Sample Output 1

2

Here is the difference for each of the four pair of an element of A and an element of B: \lvert 1-4\rvert=3, \lvert 1-9\rvert=8, \lvert 6-4\rvert=2, and \lvert 6-9\rvert=3. We should print the minimum of these values, or 2.

Sample Input 2

1 1
10
10

Sample Output 2

0

Sample Input 3

6 8
82 76 82 82 71 70
17 39 67 2 45 35 22 24

Sample Output 3

3

Problem Statement

We have a grid with H horizontal rows and W vertical columns. We denote by (i,j) the cell at the i-th row from the top and j-th column from the left. Each cell in the grid has a lowercase English letter written on it. The letter written on (i,j) equals the j-th character of a given string S_i.

Snuke will repeat moving to an adjacent cell sharing a side to travel from (1,1) to (H,W). Determine if there is a path in which the letters written on the visited cells (including initial (1,1) and final (H,W)) are s \rightarrow n \rightarrow u \rightarrow k \rightarrow e \rightarrow s \rightarrow n \rightarrow \dots, in the order of visiting. Here, a cell (i_1,j_1) is said to be an adjacent cell of (i_2,j_2) sharing a side if and only if |i_1-i_2|+|j_1-j_2| = 1.

Formally, determine if there is a sequence of cells ((i_1,j_1),(i_2,j_2),\dots,(i_k,j_k)) such that:

• (i_1,j_1) = (1,1),(i_k,j_k) = (H,W);
• (i_{t+1},j_{t+1}) is an adjacent cell of (i_t,j_t) sharing a side, for all t\ (1 \leq t < k); and
• the letter written on (i_t,j_t) coincides with the (((t-1) \bmod 5) + 1)-th character of snuke, for all t\ (1 \leq t \leq k).

Constraints

• 2\leq H,W \leq 500
• H and W are integers.
• S_i is a string of length W consisting of lowercase English letters.

Sample Input 1

2 3
sns
euk

Sample Output 1

Yes

The path (1,1) \rightarrow (1,2) \rightarrow (2,2) \rightarrow (2,3) satisfies the conditions because they have s \rightarrow n \rightarrow u \rightarrow k written on them, in the order of visiting.

Sample Input 2

2 2
ab
cd

Sample Output 2

No

Sample Input 3

5 7
skunsek
nukesnu
ukeseku
nsnnesn
uekukku

Sample Output 3

Yes