There is rectangle of size 𝑁×𝑀N×M with opposite corners at (0,0)(0,0) and (𝑁,𝑀)(N,M); and a special point (𝑥+0.5,𝑦+0.5) (0≤𝑥<𝑁,0≤𝑦<𝑀)(x+0.5,y+0.5) (0≤x<N,0≤y<M).Two players play a game on the rectangle where each player takes alternate turns. In his/her turn, the player will choose a line, either 𝑥=𝑘x=k or 𝑦=𝑘y=k, such that:𝑘k is an integer;The chosen line divides the current rectangle into two non-empty parts.The part of rectangle that does not consist of the special point, is discarded for further moves.The player who cannot make a move loses. If both players play optimally, determine the number of special points such that the first player wins.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case contains two space-separated integers 𝑁N and 𝑀M — the lengths of the sides of the rectangle.Output FormatFor each test case, print the number of special points (𝑥+0.5,𝑦+0.5)(x+0.5,y+0.5) for which the first player wins the game.Note that 0≤𝑥<𝑁0≤x<N and 0≤𝑦<𝑀0≤y<M.Constraints1≤𝑇≤1041≤T≤10 4 1≤𝑁,𝑀≤1061≤N,M≤10 6 The sum of 𝑁N as well as the sum of 𝑀M over all test cases does not exceed 10610 6 .Sample 1:InputOutput42 12 23 51 120100Explanation:Test case 11 : There are 22 possible special points (0.5,0.5)(0.5,0.5) and (1.5,0.5)(1.5,0.5). In both cases, the first player can select the line 𝑥=1x=1 on his first move, and then the second player is left with no moves. Thus, the first player wins for both the special points.Test case 22 : There are 44 possible special points, all of them end up losing for the first player.

A game is played by moving a game piece left or right along a horizontal game board. The board consists of spaces of various colors, as shown. The circle represents the initial location of the game piece.Yellow Black Green Green Red Yellow Black Black Yellow Black                  ● The following algorithm indicates how the game is played. The game continues until the game is either won by landing on the red space or lost when the piece moves off either end of the board.Step 1:Place a game piece on a space that is not red and set a counter to 0.Step 2:If the game piece is on a yellow space, move the game piece 3 positions to the left and go to step 3. Otherwise, if the game piece is on a black space, move the game piece 1 position to the left and go to step 3. Otherwise, if the game piece is on a green space, move the game piece 2 positions to the right and go to step 3.Step 3:Increase the value of the counter by 1.Step 4:If game piece is on the red space or moved off the end of the game board, the game is complete. Otherwise, go back to step 2.If a game is begun by placing the game piece on the rightmost black space for step 1, what will be the value of the counter at the end of the game?Responses2233445

We are given a two-dimensional board of size N × M (N rows and M columns). Each field of the board can be empty ('.'), may contain an obstacle ('X') or may have a character in it. The character might be either an assassin ('A') or a guard. Each guard stands still and looks straight ahead, in the direction they are facing.Every guard looks in one of four directions (up, down, left or right on the board) and is represented by one of four symbols. A guard denoted by '<' is looking to the left; by '>', to the right; '^', up; or 'v', down. The guards can see everything in a straight line in the direction in which they are facing, as far as the first obstacle ('X' or any other guard) or the edge of the board.The assassin can move from the current field to any other empty field with a shared edge. The assassin cannot move onto fields containing obstacles or enemies.Write a function:bool solution(vector<string> &B);that, given an array B consisting of N strings denoting rows of the array, returns true if is it possible for the assassin to sneak from their current location to the bottom-right cell of the board undetected, and false otherwise.Examples:1. Given B = ["X.....>", "..v..X.", ".>..X..", "A......"], your function should return false. All available paths lead through a field observed by a guard.2. Given B = ["...Xv", "AX..^", ".XX.."], your function should return true. The guard in the second row is blocking the other one from watching the bottom-right square.3. Given B = ["...", ">.A"], your function should return false, as the assassin gets spotted right at the start.4. Given B = ["A.v", ..."], your function should return false. It's not possible for the assassin to enter the bottom-right cell undetected, as the cell is observed.Write an efficient algorithm for the following assumptions:N is an integer within the range [1..500];all strings in B are of the same length M from range [1..500];there is exactly one assassin on the board;there is no guard or wall on B[N−1][M−1];every string in B consists only of the following characters '.', 'X', '<', '>', 'v', '^' and/or 'A'.

In the following game, in which s1 = (p, 1 − p) is Player 1’s strategy and s2 = (q, 1 − q) isPlayer 2’s strategy, Player 2 is indifferent between L and R when p is equal to: [Write you answeras a decimal number, e.g. 0.33]q 1 − qL Rp U 0, 0 3,31 − p D 1, 1 0,0

Two kittens, Max and Min, play with a pair of non-negative integers x and y. As you can guess from their names, kitten Max loves to maximize and kitten Min loves to minimize. As part of this game Min wants to make sure that both numbers, x and y became negative at the same time, and kitten Max tries to prevent him from doing so.Each kitten has a set of pairs of integers available to it. Kitten Max has n pairs of non-negative integers (ai, bi) (1 ≤ i ≤ n), and kitten Min has m pairs of non-negative integers (cj, dj) (1 ≤ j ≤ m). As kitten Max makes a move, it can take any available pair (ai, bi) and add ai to x and bi to y, and kitten Min can take any available pair (cj, dj) and subtract cj from x and dj from y. Each kitten can use each pair multiple times during distinct moves.Max moves first. Kitten Min is winning if at some moment both numbers a, b are negative simultaneously. Otherwise, the winner of the game is kitten Max. Determine which kitten wins if both of them play optimally.InputThe first line contains two integers, n and m (1 ≤ n, m ≤ 100 000) — the number of pairs of numbers available to Max and Min, correspondingly.The second line contains two integers x, y (1 ≤ x, y ≤ 109) — the initial values of numbers with which the kittens are playing.Next n lines contain the pairs of numbers ai, bi (1 ≤ ai, bi ≤ 109) — the pairs available to Max.The last m lines contain pairs of numbers cj, dj (1 ≤ cj, dj ≤ 109) — the pairs available to Min.OutputPrint «Max» (without the quotes), if kitten Max wins, or "Min" (without the quotes), if kitten Min wins.

In the following game, in which s1 = (p, 1 − p) is Player 1’s strategy and s2 = (q, 1 − q) isPlayer 2’s strategy, Player 1 is indifferent between U and D when q is equal to