Find the smallest integer $k$ with the following property:

Given any real numbers $a_{1}, a_{2} ,\ldots, a_{d}$ such that $a_{1}+a_{2}+\cdots +a_{d}=100$ and $0 \le a_{i} \le 1$ for $i=1,2,\ldots,d$ it is possible to partition these numbers into $k$ groups (some of which may be empty) such that the sum of the numbers in each group is at most 1.

The answer is 199.

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