Theory:

The Chola kingdom became weak after the death of Adhirajendra (the last king of the Vijayalaya line). Finally, the Pandya kingdom emerged as the only leading Tamil dynasty in the \(13\)th century, having Madurai as their Capital and Kayal as their great port.
Marco Polo, a famous traveller from Venice, visited Kayal twice, in 1288 and 1293. He noted that this port town was full of ships from Arabia and China and busy with trading activities.
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Marco Polo (1254-1324)
  
Sadaiyavarman Sundarapandyan:

The second ruler of the Pandyan Kingdom was Sadaiyavarman (Jatavarman) Sundarapandyan (1251 to 1268). He brought the entire Tamil Nadu under his rule, which extended up to Nellore in Andhra. Also, the Chera ruler, the chief of Malanadu, accepted his feudatory position and paid tribute to Sundarapandyan.

After the decline of the Chola rule, the Boja King of Malwa region Vira Someswara disputed Pandyas. In the war at Kannanur, Sundarapandyan defeated Someswara. Sundarapandyan also established his jurisdiction over the chieftains of Cuddalore, Kanchipuram in northern Tamil Nadu, Arcot and Salem in the western region.

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Extent of Pandya Territories under Jatavarman Sundara Pandya I (1251 - 1283 C.E.)

After Sundarapandyan, Maravarman Kulasekaran ruled successfully for 40 years, and he had two sons. The appointment of Vira Pandyan as a co-regent provoked the other son Sundara Pandyan who killed Maravarman. But in the civil war, Vira Pandyan won and firmly established his kingdom.

The defeated Sundara Pandyan escaped to Delhi and took shelter under the Ala-ud-din Khalji. This gave a chance for the invasion of Malik Kafur. After Malik Kafur’s attack, the Pandyan Kingdom divided among several kings from the main ruling Pandya’s family. Finally, in Madurai, a Muslim State subordinate to the Delhi Sultan was established.

1600px-Delhi_Sultanate_under_Khalji_dynasty_-_based_on_A_Historical_Atlas_of_South_Asia.svg.png

Maximum extent of the Delhi Sultanate under the Khalji dynasty.
Khalji territory: Dark green
Khalji vassals: Light green

Reference:

https://commons.wikimedia.org/wiki/File:ImperioPandya1251-1283AD.svg

https://commons.wikimedia.org/wiki/File:Delhi_Sultanate_under_Khalji_dynasty_-_based_on_A_Historical_Atlas_of_South_Asia.svg