{"raw_statement":[{"iden":"statement","content":"The world is actually neither a disc or a sphere. It is a ring! There are m cities there, conveniently called 0, 1, 2, ..., m - 1 and arranged on the ring in the natural order: first 0, then 1, then 2, ..., then m - 1, and then again 0 (as the world is a ring, remember?). You are given a collection of contiguous ranges of cities. Each of them starts at some city x, and contains also cities x + 1, x + 2, ..., y - 1, y, for some city y. Note that the range can wrap around, for instance if m = 5, then [3, 4, 0] is a valid range, and so are [1], [2, 3, 4], or even [3, 4, 0, 1, 2]. Your task is to choose a single city inside each range so that no city is chosen twice for two different ranges.\n\nThe input consists of several lines. The first line contains 1 ≤ T ≤ 20, the number of test cases.\n\nEach test case consists of a number of lines. The first line contains two integers 1 ≤ m ≤ 109 and 1 ≤ n ≤ 105 denoting the number of cities and the number of requests, respectively. The next n lines define the ranges: the i-th row contains two integers 0 ≤ xi, yi < m describing the i-th range .\n\nFor each test case, output one line containing YES if it is possible to assign a unique city to each request, and NO otherwise.\n\n"},{"iden":"input","content":"The input consists of several lines. The first line contains 1 ≤ T ≤ 20, the number of test cases.Each test case consists of a number of lines. The first line contains two integers 1 ≤ m ≤ 109 and 1 ≤ n ≤ 105 denoting the number of cities and the number of requests, respectively. The next n lines define the ranges: the i-th row contains two integers 0 ≤ xi, yi < m describing the i-th range ."},{"iden":"output","content":"For each test case, output one line containing YES if it is possible to assign a unique city to each request, and NO otherwise."},{"iden":"examples","content":"Input43 30 11 22 0200000 3100000 100000100001 100001100000 1000016 60 11 22 33 44 55 06 60 01 22 34 44 55 0OutputYESNOYESNO"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case:  \n- Let $ m \\in \\mathbb{Z} $ be the number of cities, labeled $ \\{0, 1, \\dots, m-1\\} $ arranged cyclically.  \n- Let $ n \\in \\mathbb{Z} $ be the number of ranges.  \n- For each $ i \\in \\{1, \\dots, n\\} $, define a circular range $ R_i = [x_i, y_i] $ as the set of cities obtained by starting at $ x_i $, moving clockwise, and including all cities up to and including $ y_i $, wrapping around if necessary.  \n\nFormally, $ R_i = \\{ (x_i + k) \\mod m \\mid k = 0, 1, \\dots, \\ell_i \\} $, where $ \\ell_i = (y_i - x_i) \\mod m $, and the size of $ R_i $ is $ |R_i| = (\\ell_i + 1) \\mod m $, with $ |R_i| \\geq 1 $.  \n\n**Constraints**  \n1. $ 1 \\leq T \\leq 20 $  \n2. For each test case:  \n   - $ 1 \\leq m \\leq 10^9 $  \n   - $ 1 \\leq n \\leq 10^5 $  \n   - $ 0 \\leq x_i, y_i < m $ for all $ i \\in \\{1, \\dots, n\\} $  \n\n**Objective**  \nDetermine whether there exists an injective function $ f: \\{1, \\dots, n\\} \\to \\{0, 1, \\dots, m-1\\} $ such that $ f(i) \\in R_i $ for all $ i \\in \\{1, \\dots, n\\} $.  \nOutput YES if such an assignment exists; otherwise, output NO.","simple_statement":"You are given a ring of m cities labeled 0 to m-1.  \nYou have n ranges, each range is a contiguous sequence of cities on the ring (can wrap around).  \nFor each range, you must pick exactly one city.  \nNo two ranges can pick the same city.  \nCan you do it? Output YES or NO.","has_page_source":false}