What is the exact origin of mochi, a traditional snack?

According to legend, during the Spring and Autumn Period and the Warring States Period, Wu Zixu, a vassal of the State of Chu, defected to the State of Wu in order to avenge his father's death, and wanted to borrow troops from the State of Wu for the purpose of crushing the State of Chu. He came to the state of Wu to help King Helu of Wu to sit on the throne and became a meritorious minister of Wu. Soon after, he realized his ambition and led the Wu troops to break through Ying, the capital of Chu, and dug up the tomb of the king of Chu and flogged his body to avenge his death. After that, Wu Zixu was appointed to the land of Shen. Once the king of Wu ordered him to lead his men to build the famous "Great City of Helu" to prevent invasion. After the construction of the city was completed, the king of Wu was overjoyed. But Wu Zixu was unhappy. He knew that he had made a lot of grudges and was afraid that someone would not be able to tolerate him in the future. When he returned to the camp, he said to his close friends, "The king will not be happy if he forgets to worry. After my death, if the country is in trouble and the people are starving, dig three feet under the Xiangmen (one of the eight city gates of Suzhou) and you will find food to feed the hungry." When Helu's son, Fu Chai, succeeded to the throne, he repeatedly rejected Wu Zixu's advice, and went so far as to listen to slanderous rumors that caused Wu Zixu to cut his own throat and die. As Wu Zixu expected, shortly after his death, Goujian of the state of Yue took the opportunity to raise an army to attack Wu and surrounded the capital city of Wu. At that time, it was the end of the year, the weather was freezing, the people in the city were deprived of food, and the starving corpses were everywhere, so the country and the people were really in danger. In this time of crisis, people remembered Wu Zixu's instructions, so they secretly demolished the walls and dug up the ground, and people were surprised to find that the foundation of the city was made of cooked glutinous rice pressed into masonry. Originally, this is Wu Zixu in the construction of the city will be a large number of glutinous rice steamed and pressed into bricks after cooling, as the cornerstone of the city wall reserve down the grain of preparedness. People couldn't help but exclaim that Wu Zixu really had foresight! People will be glutinous rice masonry clumsily up, cracked, re-steamed, divided and eaten. Later, at the end of the year in Chutian, people would use glutinous rice to make patties like the "city bricks" of that year, as a tribute to Wu Zixu. To this day, mochi is still a must-have food for people all over the South before the Spring Festival every year. In some places, the patties are made in round shapes, both large and small, to symbolize a good harvest, celebration and reunion. In some places, it is also known as rice cake, a name that also symbolizes good luck and fortune, and people often say, "Rice cake, rice cake, good year, good life". The best rice cakes are made at Taoxiangcun on Guanqian Street in Suzhou. There are lard rice cakes and brown and white sugar rice cakes with nuts. The glutinous rice flour used to make the rice cakes is fine and sweet, with a bright white color. The rice cakes can be steamed, boiled and fried, and taste fragrant and sweet. Lard rice cake and rose, osmanthus, date mud and other four varieties, its *** with the same characteristics is bright color, fat and glutinous, eaten for a long time. Our people eat rice cake has a southern style, northern style points, Suzhou rice cake is very popular in the southern style rice cake in the famous products.