A special die is so constructed that the probabilities \( \mathrm{P...

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A special die is so constructed that the probabilities
\( \mathrm{P} \) of throwing \( 1,2,3,4,5 \) and 6 are \( (1-\mathrm{K}) / 6 \),

W \( (1+2 k) / 6,(1-k) / 6,(1+k) / 6,(1-2 k) / 6 \) and \( (1+k) / 6 \), respectively. If two such dice are thrown and the probability of getting a sum equal to 9 lies between \( \frac{1}{9} \) and \( \frac{2}{9} \), then the integral value of \( k \) is
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