문제<\/h2>
Near Vlad's home, there is a pedestrian traffic light that shows the remaining time to cross the road. The number displayed by the traffic light decreases by 1 every second. However, one day, Vlad approached the crossing and could not believe his eyes: the traffic light switched from 35 to 36!<\/p>
Vlad was very surprised, but his astonishment faded in the next second: instead of 37 or any other number, the traffic light displayed something that was not a number at all. It turned out that one of the indicators of the traffic light was broken and never lit up. Hence, the number 39 looked like 35, and 38 looked like 36 (see Figures 1-3). After that, Vlad wondered: just how long can this illusion of the traffic light "ticking up by 1" every second last?<\/p>
Figures 1-3. The behavior of the traffic light from the moment it switched to 39 until the moment it switched to 37: expected is on the top, actual is on the bottom. Lit indicators are colored green (looks gray when printed in black and white), functioning but not currently lit indicators are colored white, and the broken indicator is hatched.<\/p>

[이미지 1]<\/span><\/td> [이미지 2]<\/span><\/td> [이미지 3]<\/span><\/td> <\/tr>
39 looks like 35<\/td> 38 looks like 36<\/td> 37 looks like nonsense<\/td> <\/tr> <\/tbody> <\/table>
For example, in the above situation, the illusion has lasted for exactly 1 second: from the moment the traffic light "switched from 35 to 36" (actually from 39 to 38) until the moment the traffic light started showing nonsense. Strictly speaking, the traffic light has "ticked up by 1" for $k<\/mi><\/mrow>k<\/math><\/span><\/span> k<\/span><\/span><\/span><\/span> seconds if it has consecutively displayed x<\/mi><\/mrow>x<\/math><\/span><\/span> x<\/span><\/span><\/span><\/span>, x<\/mi>+<\/mo>1<\/mn><\/mrow>x+1<\/math><\/span><\/span> x<\/span> <\/span> +<\/span> <\/span><\/span> <\/span> 1<\/span><\/span><\/span><\/span>, \dots<\/mo><\/mrow>\ldots<\/math><\/span><\/span> \dots<\/span><\/span><\/span><\/span>, x<\/mi>+<\/mo>k<\/mi><\/mrow>x+k<\/math><\/span>$

Faulty Traffic Light