4 4 4 1 0 0 1
Yes By dividing a $4 \times 4$ chocolate bar as shown in the figure below, you can obtain pieces of size $2 \times 2, 1 \times 1, 1 \times 1, 2 \times 2$. 
5 7 6 0 1 0 2 0 1
Yes By dividing a $5 \times 7$ chocolate bar as shown in the figure below, you can obtain pieces of size $1 \times 1, 2 \times 2, 1 \times 1, 4 \times 4, 1 \times 1, 2 \times 2$. 
3 2 7 0 0 0 0 0 0 0
No It is impossible to obtain seven pieces of size $1 \times 1$ from a $3 \times 2$ chocolate bar.
11 11 2 2 3
No It is impossible to obtain both a $4 \times 4$ and an $8 \times 8$ piece from an $11 \times 11$ chocolate bar.
777 777 6 8 6 9 1 2 0
Yes
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