{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv align\u003d\"left\"\u003eOn a flat table there are two circles having centers A and B, radii r_A and r_B, masses m_A and m_B and speeds v_A and v_B respectively: \u003cbr\u003e\u003ccenter\u003e\u003cimg src\u003d\"CDN_BASE_URL/853acf9d0f1d743ad96dae2300ebdf0e?v\u003d1715982541\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/center\u003e \u003cbr\u003eYou are given the initial positions, speeds, radii and masses of the circles. You have to find their positions and speeds after time t. It is guaranteed that the circles do not have any common points in the beginning and after time t. \u003cbr\u003eYou may use the following facts: \u003cbr\u003e- The speeds of the circles change only if they hit each other. \u003cbr\u003e- During a hit, the speeds may change only by vectors parallel to vector AB. \u003cbr\u003e- The values P\u003dm_A*v_A+m_B*v_B and 2E\u003dm_A*|v_A|^2+m_B*|v_B|^2 do not change all the time, including hits. \u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cbr\u003e\u003cb\u003eInput\u003c/b\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003eThe first two lines of the input contain the descriptions of circles A and B respectively. The description of a circle consists of the coordinates of its center, and its speed, its radius and mass. The coordinates are integer and do not exceed 10^4 by absolute value. The radius is a positive integer and does not exceed 10^4. The mass is a positive integer and does not exceed 100. The third line of the input contains single integer t (0 \u0026lt;\u003d t \u0026lt;\u003d 100). \u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cbr\u003e\u003cb\u003eOutput\u003c/b\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003eOutput the information about the circles after time t has passed in the same format as in the input, excluding the radius and the mass. The numbers must have at least 3 digits after the decimal point. \u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cbr\u003e\u003cb\u003eSample test(s)\u003c/b\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cbr\u003eInput\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cfont face\u003d\"Courier New\"\u003e\u003c/font\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cpre\u003e\u003c/pre\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e0 1 1 0 2 1 \u003cbr\u003e5 0 0 0 2 1 \u003cbr\u003e5 \u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cdiv align\u003d\"left\"\u003e\u003cdiv align\u003d\"left\"\u003e\u003cbr\u003eOutput\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cfont face\u003d\"Courier New\"\u003e\u003c/font\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cpre\u003e\u003c/pre\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e1.369 1.938 0.062 0.242 \u003cbr\u003e8.631 -0.938 0.938 -0.242 \u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cdiv align\u003d\"left\"\u003e\u003cdiv align\u003d\"left\"\u003e\u003cdiv align\u003d\"right\"\u003e \u003c/div\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003cdiv align\u003d\"right\"\u003e \u003c/div\u003e\u003c/div\u003e\u003cdiv align\u003d\"left\"\u003e\u003chr\u003e\u003c/div\u003e\u003ctable align\u003d\"left\" cellspacing\u003d\"7\"\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd\u003eAuthor:\u003c/td\u003e\u003ctd\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eResource:\u003c/td\u003e\u003ctd\u003eNovosibirsk SU Contest #2, by Novosibirsk Team #1 \u003cbr\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eDate:\u003c/td\u003e\u003ctd\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003c/div\u003e \u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\r\n\u003c/div\u003e"}}]}