{"raw_statement":[{"iden":"problem statement","content":"Takahashi is on an $xy$\\-plane. Initially, he is at point $(s _ x,s _ y)$, and he wants to reach point $(t _ x,t _ y)$.\nOn the $xy$\\-plane is a rectangle $R\\coloneqq\\lbrace(x,y)\\mid a-0.5\\leq x\\leq b+0.5,c-0.5\\leq y\\leq d+0.5\\rbrace$. Consider the following operation:\n\n*   Choose a lattice point $(x,y)$ contained in the rectangle $R$. Takahashi teleports to the point symmetric to his current position with respect to point $(x,y)$.\n\nDetermine if he can reach point $(t _ x,t _ y)$ after repeating the operation above between $0$ and $10^6$ times, inclusive. If it is possible, construct a sequence of operations that leads him to point $(t _ x,t _ y)$."},{"iden":"constraints","content":"*   $0\\leq s _ x,s _ y,t _ x,t _ y\\leq2\\times10^5$\n*   $0\\leq a\\leq b\\leq2\\times10^5$\n*   $0\\leq c\\leq d\\leq2\\times10^5$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$s _ x$ $s _ y$\n$t _ x$ $t _ y$\n$a$ $b$ $c$ $d$"},{"iden":"sample input 1","content":"1 2\n7 8\n7 9 0 3"},{"iden":"sample output 1","content":"Yes\n7 0\n9 3\n7 1\n8 1\n\nFor example, the following choices lead him from $(1,2)$ to $(7,8)$.\n\n*   Choose $(7,0)$. Takahashi moves to $(13,-2)$.\n*   Choose $(9,3)$. Takahashi moves to $(5,8)$.\n*   Choose $(7,1)$. Takahashi moves to $(9,-6)$.\n*   Choose $(8,1)$. Takahashi moves to $(7,8)$.\n\n![image](https://img.atcoder.jp/abc289/d6d2cc458bbc92e975ba267856f673cf.png)\nAny output that satisfies the conditions is accepted; for example, printing\n\nYes\n7 3\n9 0\n7 2\n9 1\n8 1\n\nis also accepted.\n![image](https://img.atcoder.jp/abc289/3faa56b1d245b87bd4cc36083495383c.png)"},{"iden":"sample input 2","content":"0 0\n8 4\n5 5 0 0"},{"iden":"sample output 2","content":"No\n\nNo sequence of operations leads him to point $(8,4)$.\n![image](https://img.atcoder.jp/abc289/eb363d09e74f89c5474a4fc7529308bc.png)"},{"iden":"sample input 3","content":"1 4\n1 4\n100 200 300 400"},{"iden":"sample output 3","content":"Yes\n\nTakahashi may already be at the destination in the beginning."},{"iden":"sample input 4","content":"22 2\n16 7\n14 30 11 14"},{"iden":"sample output 4","content":"No"}],"translated_statement":[{"iden":"problem statement","content":"高桥在 $xy$ 平面上。初始时，他位于点 $(s _ x,s _ y)$，他希望到达点 $(t _ x,t _ y)$。\n在 $xy$ 平面上有一个矩形 $R\\coloneqq\\lbrace(x,y)\\mid a-0.5\\leq x\\leq b+0.5,c-0.5\\leq y\\leq d+0.5\\rbrace$。考虑以下操作：\n\n* 选择矩形 $R$ 中的一个格点 $(x,y)$。高桥瞬移到他当前位置关于点 $(x,y)$ 的对称点。\n\n判断他是否能在重复上述操作 $0$ 到 $10^6$ 次（含）后到达点 $(t _ x,t _ y)$。如果可以，请构造一个操作序列，使其到达点 $(t _ x,t _ y)$。"},{"iden":"constraints","content":"* $0\\leq s _ x,s _ y,t _ x,t _ y\\leq2\\times10^5$\n* $0\\leq a\\leq b\\leq2\\times10^5$\n* $0\\leq c\\leq d\\leq2\\times10^5$\n* 输入中的所有值均为整数。"},{"iden":"input","content":"输入从标准输入按以下格式给出：\n\n$s _ x$ $s _ y$\n$t _ x$ $t _ y$\n$a$ $b$ $c$ $d$"},{"iden":"sample input 1","content":"1 2\n7 8\n7 9 0 3"},{"iden":"sample output 1","content":"Yes\n7 0\n9 3\n7 1\n8 1\n\n例如，以下选择可将高桥从 $(1,2)$ 移动到 $(7,8)$：\n\n* 选择 $(7,0)$。高桥移动到 $(13,-2)$。\n* 选择 $(9,3)$。高桥移动到 $(5,8)$。\n* 选择 $(7,1)$。高桥移动到 $(9,-6)$。\n* 选择 $(8,1)$。高桥移动到 $(7,8)$。\n\n![image](https://img.atcoder.jp/abc289/d6d2cc458bbc92e975ba267856f673cf.png)\n任何满足条件的输出均可接受；例如，输出\n\nYes\n7 3\n9 0\n7 2\n9 1\n8 1\n\n也是可接受的。\n![image](https://img.atcoder.jp/abc289/3faa56b1d245b87bd4cc36083495383c.png)"},{"iden":"sample input 2","content":"0 0\n8 4\n5 5 0 0"},{"iden":"sample output 2","content":"No\n\n没有任何操作序列能将他带到点 $(8,4)$。\n![image](https://img.atcoder.jp/abc289/eb363d09e74f89c5474a4fc7529308bc.png)"},{"iden":"sample input 3","content":"1 4\n1 4\n100 200 300 400"},{"iden":"sample output 3","content":"Yes\n\n高桥初始时可能已在目标位置。"},{"iden":"sample input 4","content":"22 2\n16 7\n14 30 11 14"},{"iden":"sample output 4","content":"No"}],"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}