The demand strength in India's services sector promoted the fastest increases in new business and output in close to 13 years, a private survey showed on Wednesday. Along with robust domestic demand, international demand was strong as the sub-index rose to a four-month peak and business optimism hit its highest since December. The input prices index was at a three-month high from a 2-1/2-year low in March and firms raised their charges at the fastest pace this year. The prices charged index rose to 53.5 from 52.4.