Problem Statement

You are given an integer N and a sequence A=(A _ 1,A _ 2,\ldots,A _ N) of length N.

Given Q queries, process them in the given order. Each query is of one of the following two kinds:

• 1 k x : set the value A _ k to x.
• 2 k : print the value A _ k.

Constraints

• 1 \leq N \leq 10 ^ 5
• 1 \leq Q \leq 10 ^ 5
• 0 \leq A _ i \leq 10 ^ 9\ (1\leq i\leq N)
• 1\leq k\leq N for all queries.
• 0\leq x\leq 10 ^ 9 for all queries of the first kind.
• There is at least one query of the second kind.
• All values in the input are integers.

Sample Input 1

3
1 3 5
7
2 2
2 3
1 3 0
2 3
1 2 8
2 2
2 1

Sample Output 1

3
5
0
8
1

Initially, A=(1,3,5).

• For the 1-st query, A=(1,3,5), where A _ 2=3, so 3 should be printed.
• For the 2-nd query, A=(1,3,5), where A _ 3=5, so 5 should be printed.
• The 3-rd query sets the value A _ 3 to 0, making A=(1,3,0).
• For the 4-th query, A=(1,3,0), where A _ 3=0, so 0 should be printed.
• The 5-th query sets the value A _ 2 to 8, making A=(1,8,0).
• For the 6-th query, A=(1,8,0), where A _ 2=8, so 8 should be printed.
• For the 7-th query, A=(1,8,0), where A _ 1=1, so 1 should be printed.

Sample Input 2

5
22 2 16 7 30
10
1 4 0
1 5 0
2 2
2 3
2 4
2 5
1 4 100
1 5 100
2 3
2 4

Sample Output 2

2
16
0
0
16
100

Sample Input 3

7
478 369 466 343 541 42 165
20
2 1
1 7 729
1 6 61
1 6 838
1 3 319
1 4 317
2 4
1 1 673
1 3 176
1 5 250
1 1 468
2 6
1 7 478
1 5 595
2 6
1 6 599
1 6 505
2 3
2 5
2 1

Sample Output 3

478
317
838
838
176
595
468

Problem Statement

You are given integers L, R, and a string S consisting of lowercase English letters.
Print this string after reversing (the order of) the L-th through R-th characters.

Constraints

• S consists of lowercase English letters.
• 1 \le |S| \le 10^5 (|S| is the length of S.)
• L and R are integers.
• 1 \le L \le R \le |S|

Sample Input 1

3 7
abcdefgh

Sample Output 1

abgfedch

After reversing the 3-rd through 7-th characters of abcdefgh, we have abgfedch.

Sample Input 2

1 7
reviver

Sample Output 2

reviver

The operation may result in the same string as the original.

Sample Input 3

4 13
merrychristmas

Sample Output 3

meramtsirhcyrs

Problem Statement

There is a grid with H horizontal rows and W vertical columns. For two integers i and j such that 1 \leq i \leq H and 1 \leq j \leq W, the square at the i-th row from the top and j-th column from the left (which we denote by (i, j)) has an integer A_{i, j} written on it.

Takahashi is currently at (1,1). From now on, he repeats moving to an adjacent square to the right of or below his current square until he reaches (H, W). When he makes a move, he is not allowed to go outside the grid.

Takahashi will be happy if the integers written on the squares he visits (including initial (1, 1) and final (H, W)) are distinct. Find the number of his possible paths that make him happy.

Constraints

• 2 \leq H, W \leq 10
• 1 \leq A_{i, j} \leq 10^9
• All values in the input are integers.

Sample Input 1

3 3
3 2 2
2 1 3
1 5 4

Sample Output 1

3

There are six possible paths:

• (1, 1) \rightarrow (1, 2) \rightarrow (1, 3) \rightarrow (2, 3) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 2, 3, 4, so he will not be happy.
• (1, 1) \rightarrow (1, 2) \rightarrow (2, 2) \rightarrow (2, 3) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 3, 4, so he will not be happy.
• (1, 1) \rightarrow (1, 2) \rightarrow (2, 2) \rightarrow (3, 2) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 5, 4, so he will be happy.
• (1, 1) \rightarrow (2, 1) \rightarrow (2, 2) \rightarrow (2, 3) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 3, 4, so he will not be happy.
• (1, 1) \rightarrow (2, 1) \rightarrow (2, 2) \rightarrow (3, 2) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 5, 4, so he will be happy.
• (1, 1) \rightarrow (2, 1) \rightarrow (3, 1) \rightarrow (3, 2) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 5, 4, so he will be happy.

Thus, the third, fifth, and sixth paths described above make him happy.

Sample Input 2

10 10
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Sample Output 2

48620

In this example, every possible path makes him happy.

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

You are given non-negative integers a, b, and C. Determine if there is a pair of non-negative integers (X, Y) that satisfies all of the following five conditions. If such a pair exists, print one.

• 0 \leq X < 2^{60}
• 0 \leq Y < 2^{60}
• \operatorname{popcount}(X) = a
• \operatorname{popcount}(Y) = b
• X \oplus Y = C

Here, \oplus denotes the bitwise XOR.

If multiple pairs (X, Y) satisfy the conditions, you may print any of them.

Constraints

• 0 \leq a \leq 60
• 0 \leq b \leq 60
• 0 \leq C < 2^{60}
• All input values are integers.

Sample Input 1

3 4 7

Sample Output 1

28 27

The pair (X, Y) = (28, 27) satisfies the conditions. Here, X and Y in binary are 11100 and 11011, respectively.

• X in binary is 11100, so \operatorname{popcount}(X) = 3.
• Y in binary is 11011, so \operatorname{popcount}(Y) = 4.
• X \oplus Y in binary is 00111, so X \oplus Y = 7.

If multiple pairs of non-negative integers satisfy the conditions, you may print any of them, so printing 42 45, for example, would also be accepted.

Sample Input 2

34 56 998244353

Sample Output 2

-1

No pair of non-negative integers satisfies the conditions.

Sample Input 3

39 47 530423800524412070

Sample Output 3

540431255696862041 10008854347644927

Note that the values to be printed may not fit in 32-bit integers.