Statement

After reading about the ambitious SETI program, William decided to join the project and build an array of N radios for interstellar transmissions in his garage. However, the array has not received any extraterrestrial message yet, fact that William blamed to the phenomenon of interference. In particular, William noticed that whenever the i-th radio is turned on, V_i of the radios on its left (that is, radios j = i-V_i … i-1) receive disturbed signals and are not usable. Fortunately, no interfering signals are received by radios on the right (that is, with j > i). In order to plan his next experiment avoiding interferences, William now needs to select a subset of his radios avoiding interferences, that is, such that if radio i is turned on then all radios between i-V_i and i-1 are turned off. Help William plan his next experiment, by counting the number of subsets of radios avoiding interferences modulo in C/C++ and mod in Pascal. 1000000007.