Question: Which battle took place first , Battle of Pusan Perimeter or Second Battle of the Marne ?

Context paragraphs:
15th Division (North Korea): The 15th Infantry Division was a military formation of the Korean People's Army during the 20th Century.  The division fought in the 1950 Korean War; it took part in the North Korean advance from Seoul to Taejon, and fought in the Battle of Pusan Perimeter.  The 15th Division fought along the eastern coast, above Pusan, eventually being annihilated.

Hill 303 massacre: The Hill 303 massacre (Korean: 303 고지 학살 사건 ) was a war crime that took place during the Korean War on August 17, 1950, on a hill above Waegwan, South Korea.  Forty-one United States Army prisoners of war were shot and killed by troops of the North Korean army during one of the smaller engagements of the Battle of Pusan Perimeter.

Bloody Gulch massacre: The Bloody Gulch massacre was a war crime that took place in the Korean War on August 12, 1950 in "Bloody Gulch", west of Masan, South Korea.  After a very successful attack on two undefended US Artillery Battalions that killed or wounded hundreds of US troops, members of the North Korean People's Army (KPA) 13th Regiment executed seventy-five captured US Army prisoners of war during one of the smaller engagements of the Battle of Pusan Perimeter.  The troops were from the 555th Field Artillery Battalion (24th Infantry Division) and the 90th Field Artillery Battalion (25th Infantry Division).

Second Battle of Naktong Bulge: The Second Battle of Naktong Bulge was an engagement between United Nations (UN) and North Korean (NK) forces early in the Korean War from September 1 to September 15, 1950, along the Naktong River in South Korea.  It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously.  The battle ended in a victory for the United Nations after large numbers of United States (US) and Republic of Korea (ROK) troops repelled a strong North Korean attack.

Battle of the Bowling Alley: In the Battle of the Bowling Alley (August 12–25, 1950), United Nations (UN) forces defeated North Korean forces early in the Korean War near the city of Taegu, South Korea.  The battle took place in a narrow valley, dubbed the "Bowling Alley", which was north of Taegu.  It followed a week of fighting between the Korean People's Army (KPA) 13th Division and the Republic of Korea Army's (ROK) 1st Division along the latter's last defensible line in the hills north of the city.  Reinforcements, including the US Army's 27th and 23rd Infantry Regiments were committed to bolster the South Koreans' defenses.  This battle and several others were smaller engagements of the Battle of Pusan Perimeter.

Battle of Pusan Perimeter: The Battle of Pusan Perimeter was a large-scale battle between United Nations and North Korean forces lasting from August 4 to September 18, 1950.  It was one of the first major engagements of the Korean War.  An army of 140,000 UN troops, having been pushed to the brink of defeat, were rallied to make a final stand against the invading North Korean army, 98,000 men strong.

First Battle of Naktong Bulge: The First Battle of Naktong Bulge was an engagement between United States and North Korean forces early in the Korean War from August 5–19, 1950 in the vicinity of Yongsan (Yeongsan, Changnyeong county) and the Naktong River in South Korea.  It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously.  The battle ended in a victory for the United States after large numbers of US reinforcements destroyed an attacking North Korean division.

Eighth Army Ranger Company: The Eighth Army Ranger Company, also known as the 8213th Army Unit, was a Ranger light infantry company of the United States Army that was active during the Korean War.  As a small special forces unit, it specialized in irregular warfare.  Intended to combat the North Korean (NK) commandos who had been effective at infiltration and disruption behind United Nations (UN) lines, the Eighth Army Ranger Company was formed at the height of the Battle of Pusan Perimeter in September 1950 and was the first U.S. Army Ranger unit created since World War II.  The company went into action as a part of the 25th Infantry Division during the UN advance into North Korea in October and November.  It was best known for its defense of Hill 205 against an overwhelming Chinese attack during the Battle of the Ch'ongch'on River which resulted 41 of the 51 Rangers becoming casualties.

Battle of Masan: The Battle of Masan was an engagement between United Nations (UN) and North Korean (NK) forces, which took place early in the Korean War between August 5 and September 19, 1950, in the vicinity of Masan and the Naktong River in South Korea.  It was part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously.  The battle ended in a victory for the UN after large numbers of United States (US) and Republic of Korea (ROK) troops were able to repel the repeated attacks of two North Korean divisions.

Second Battle of the Marne: The Second Battle of the Marne (French: "Seconde Bataille de la Marne" ), or "Battle of Reims" (15 July – 6 August 1918) was the last major German offensive on the Western Front during the First World War.  The attack failed when an Allied counterattack by French and American forces, including several hundred tanks, overwhelmed the Germans on their right flank, inflicting severe casualties.  The German defeat marked the start of the relentless Allied advance which culminated in the Armistice with Germany about 100 days later.

Supporting paragraphs: Second Battle of the Marne Battle of Pusan Perimeter
Answer: Second Battle of the Marne