Charlie and the Chocolate Factory

Charlie, a chocolate enthusiast, has been tasked with cutting a large chocolate bar into smaller segments at Willy Wonka's Chocolate Factory. The bar has specific cut marks indicating the lengths of the required segments. These lengths are provided as an array, representing the segments to be cut from the bar. The order of the lengths in the array corresponds to the arrangement of the segments on the initial bar, from its left endpoint to its right endpoint. $($The initial bar is a large segment itself.$)$ Willy Wonka's cutting machine can only handle segments that are at least a certain length, which we'll call minSegmentLength. Please help Charlie determine if it's possible to cut the bar into the given segments, using only the cutting machine available in the factory.

Example: $n=3,$ lengths $=[70,10,60],$ minSegmentLength $=80$

The total length of the initial bar is $70+10+60=140$ units, which is greater than $80.$ So Charlie can use the cutting machine to cut the initial segment into two segments of lengths $70+10=80$ and $60.$ Then Charlie can cut the first segment $($since its length is equal to minSegmentLength$)$ into two segments of lengths $70$ and $10,$ thus obtaining the three required segments. Therefore, return 'Possible'.

Example: $n=3,$ lengths $=[70,5,60],$ minSegmentLength $=80$

The total length of the bar is $70+5+60=135$ units. Charlie can cut this initial bar since its length is at least minSegmentLength $=80.$ However, no matter how he performs the initial cut, he will be left with a segment that still needs to be cut, but that has a length less than $80$: He can cut along the first cutting mark and get two segments of length $70$ and $65.$ The segment of length $65$ needs to be cut further because it has the second cutting mark, but its length is less than $80.$ Alternatively, he can cut along the second cut and get two segments of lengths $75$ and $60.$ Now the first segment needs to be cut further, but its length is less than $80.$ Therefore, return 'Impossible'.

Constraints:

$2n{10}^5$

$1$min SegmentLength ${10}^9$

$1$ lengths string HelpCharlie$($vector lengths, int minSegmentLength$))$