A ternary string is a sequence of digits, where each digit is either 0, 1, or 2.Chiaki has a ternary string s which can self-reproduce. Every second, a digit 0 is inserted after every 1 in the string, and then a digit 1 is inserted after every 2 in the string, and finally the first character will disappear.For example, ``212'' will become ``11021'' after one second, and become ``01002110'' after another second.Chiaki would like to know the number of seconds needed until the string become an empty string. As the answer could be very large, she only needs the answer modulo .
A ternary string is a sequence of digits, where each digit is either 0, 1, or 2. Chiaki has a ternary string s which can self-reproduce. Every second, a digit 0 is inserted after every 1 in the string, and then a digit 1 is inserted after every 2 in the string, and finally the first character will disappear. For example, ``212'' will become ``11021'' after one second, and become ``01002110'' after another second. Chiaki would like to know the number of seconds needed until the string become an empty string. As the answer could be very large, she only needs the answer modulo (109 + 7).
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